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Dissertations / Theses on the topic 'Orlicz spaces'
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Al-Rashed, Maryam Houmod Ali. "Noncommutative Orlicz spaces." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434998.
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Cazacu, Constantin Dan. "Twisted sums of Orlicz spaces /." free to MU campus, to others for purchase, 1998. http://wwwlib.umi.com/cr/mo/fullcit?p9901223.
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Szab?o, L?aszl?o. "On ergodic and Martingale theorems in Orlicz spaces /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683756124057.
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Doto, James William. "Conditional uniform convexity in Orlicz spaces and minimization problems." Thesis, Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/27352.
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El-Mabrouk, Khalifa. "Semilinear perturbations of harmonic spaces and Martin-Orlicz capacities an approach to the trace of moderate U-functions /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964456435.
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Lai, Wei-Kai. "The radon-nikodym property for the Wittstock and Fremlin tensor products of orlicz sequence spaces and banach lattices /." Full text available from ProQuest UM Digital Dissertations, 2008. http://0-proquest.umi.com.umiss.lib.olemiss.edu/pqdweb?index=0&did=1850496461&SrchMode=1&sid=1&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1277325845&clientId=22256.
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Capolli, Marco. "Selected Topics in Analysis in Metric Measure Spaces." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/288526.
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The thesis is composed by three sections, each devoted to the study of a specific problem in the setting of PI spaces. The problem analyzed are: a C^m Lusin approximation result for horizontal curves in the Heisenberg group, a limit result in the spirit of Burgain-Brezis-Mironescu for Orlicz-Sobolev spaces in Carnot groups and the differentiability of Lipschitz functions in Laakso spaces.
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Capolli, Marco. "Selected Topics in Analysis in Metric Measure Spaces." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/288526.
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The thesis is composed by three sections, each devoted to the study of a specific problem in the setting of PI spaces. The problem analyzed are: a C^m Lusin approximation result for horizontal curves in the Heisenberg group, a limit result in the spirit of Burgain-Brezis-Mironescu for Orlicz-Sobolev spaces in Carnot groups and the differentiability of Lipschitz functions in Laakso spaces.
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Carvalho, Marcos Leandro Mendes. "Equações diferenciais parciais elípticas multivalentes: crescimento crítico, métodos variacionais." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3686.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work we develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity, minimization and compactness techniques to investigate existence of solution of the multivalued equation −∆Φu ∈ ∂ j(.,u) +λh in Ω, where Ω ⊂ RN is a bounded domain with boundary smooth ∂Ω, Φ : R → [0,∞) is a suitable N-function, ∆Φ is the corresponding Φ−Laplacian, λ > 0 is a parameter, h : Ω → R is a measurable and ∂ j(.,u) is a Clarke’s Generalized Gradient of a function u %→ j(x,u), a.e. x ∈ Ω, associated with critical growth. Regularity of the solutions is investigated, as well.
Neste trabalho desenvolvemos argumentos sobre a teoria de pontos críticos para funcionais Localmente Lipschitz em Espaços de Orlicz-Sobolev, juntamente com técnicas de convexidade, minimização e compacidade para investigar a existencia de solução da equação multivalente −∆Φu ∈ ∂ j(.,u) +λh em Ω, onde Ω ⊂ RN é um domínio limitado com fronteira ∂Ω regular, Φ : R → [0,∞) é uma N-função apropriada, ∆Φ é o correspondente Φ−Laplaciano, λ > 0 é um parâmetro, h : Ω → R é uma função mensurável e ∂ j(.,u) é o gradiente generalizado de Clarke da função u %→ j(x,u), q.t.p. x ∈ Ω, associada com o crescimento crítico. A regularidade de solução também será investigada.
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Kumar, Vishvesh. "Harmonic analysis on Orlicz spaces for certain hypergroups and on discrete hypergroups arising from semigroups with emphasis on Ramsey theory." Thesis, IIT Delhi, 2019. http://eprint.iitd.ac.in:80//handle/2074/8075.
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MENESES, João Paulo Formiga de. "Existência de múltiplas soluções positivas para uma classe de problemas elípticos quaselineares." Universidade Federal de Campina Grande, 2016. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1425.
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Neste trabalho, utilizando sub e supersoluções e métodos variacionais sobre espaços de Orlicz-Sobolev, estudamos a existência de múltiplas soluções positivas para uma classe de problemas elípticos quaselineares.
In this work, using sub and supersolutions and variational methods on Orlicz-Sobolev spaces, we study the existence of multiple positive solutions for a class of quasilinear elliptic problems.
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Silva, Ailton Rodrigues da. "Existência, multiplicidade e concentração de soluções positivas para uma classe de problemas quasilineares em espaços de Orlicz-Sobolev." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9258.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work we establish existence, multiplicity and concentration of positive solutions for the following class of problem 8<: div 2 ( jruj)ru + V (x) (juj)u = f(u); in RN; u 2 W1; (RN); u > 0 in RN; where N 2, is a positive parameter, ; V; f are functions satisfying technical conditions that will be presented throughout the thesis and (t) = Rjtj 0 (s)sds. The main tools used are Variational methods, Lusternik-Schnirelman of category, Penalization methods and properties of Orlicz-Sobolev spaces.
Neste trabalho estabelecemos resultados de existência, multiplicidade e concentração de soluções positivas para a seguinte classe de problemas quasilineares 8<: div 2 ( jruj)ru + V (x) (juj)u = f(u); em RN; u 2 W1; (RN); u > 0 em RN; onde N 2, é um parâmetro positivo, ; V; f são funções satisfazendo condições técnicas que serão apresentadas ao longo da tese e (t) = Rjtj 0 (s)sds. As principais ferramentas utilizadas são os Métodos Variacionais, Categoria de Lusternik-Schnirelman, Método de Penalização e propriedades dos espaços de Orlicz-Sobolev.
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Carvalho, Gilson Mamede de. "Equações de Schrödinger quaselineares com potenciais singulares ou se anulando no infinito." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9254.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we study existence of standing wave solution for a class of quasilinear Schrödinger equations involving potentials that may be singular at the origin or vanishing at infinity. For dimensions bigger than two, we consider nonlinearities with subcritical growth. In dimension two, we work with nonlinearities having exponential critical growth. To obtain our results, we have used variational techniques, more specifically, a version of the Mountain Pass Theorem, a regularity result of Brézis-Kato type, arguments of symmetrical criticality principle type, Moser iteration method and a Trudinger-Moser type inequality.
Neste trabalho, estudamos existência de solução do tipo onda estacionária para uma classe de equações de Schrödinger quaselineares, envolvendo pontencias que podem ser singular na origem ou que podem se anular no infinito. Para dimensões maiores que dois, consideramos não-linearidades com crescimento subcrítico. Em dimensão dois, trabalhamos com não linearidades possuindo crescimente crítico exponencial. Para a obtenção de nossos resultados, usamos técnicas variacionais, mais especificamente, uma versão do Teorema do Passo da Montanha, um resultado de regularidade do tipo Brézis- Kato, argumentos do tipo princípio da criticalidade simétrica, método de iteração de Moser e uma desigualdade do tipo Trudinger-Moser.
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Zghal, Mohamed Khalil. "Inégalités de type Trudinger-Moser et applications." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1077/document.
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Cette thèse porte sur quelques inégalités de type Trudinger-Moser et leurs applications à l'étude des injections de Sobolev qu'elles induisent dans les espaces d'Orlicz et à l'analyse d'équations aux dérivées partielles non linéaires à croissance exponentielle.Le travail qu'on présente ici se compose de trois parties. La première partie est consacrée à la description du défaut de compacité de l'injection de Sobolev 4D dans l'espace d'Orlicz dansle cadre radial.L'objectif de la deuxième partie est double. D'abord, on caractérise le défaut de compacité de l'injection de Sobolev 2D dans les différentes classes d'espaces d'Orlicz. Ensuite, on étudiel'équation de Klein-Gordon semi-linéaire avec non linéarité exponentielle, où la norme d'Orlicz joue un rôle crucial. En particulier, on aborde les questions d'existence globale, de complétude asymptotique et d'étude qualitative.Dans la troisième partie, on établit des inégalités optimales de type Adams, en étroite relation avec les inégalités de Hardy, puis on fournit une description du défaut de compacité des injections de Sobolev qu'elles induisentThis thesis focuses on some Trudinger-Moser type inequalities and their applications to the study of Sobolev embeddings they induce into the Orlicz spaces, and the investigation of nonlinear partial differential equations with exponential growth.The work presented here includes three parts. The first part is devoted to the description of the lack of compactness of the 4D Sobolev embedding into the Orlicz space in the radialframework.The aim of the second part is twofold. Firstly, we characterize the lack of compactness of the 2D Sobolev embedding into the different classes of Orlicz spaces. Secondly, we undertakethe study of the nonlinear Klein-Gordon equation with exponential growth, where the Orlicz norm plays a crucial role. In particular, issues of global existence, scattering and qualitativestudy are investigated.In the third part, we establish sharp Adams-type inequalities invoking Hardy inequalities, then we give a description of the lack of compactness of the Sobolev embeddings they induce
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Ben, Ayed Inès. "Etude d'injections de Sobolev critiques dans les espaces d'Orlicz et applications." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1133.
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Dans cette thèse, on s'est attaché d'une part à d'écrire le défaut de compacité de l'injection de Sobolev critique dans les différentes classes d'espaces d'Orlicz, et d'autre part à étudier l'équation de Klein-Gordon avec une non-linéarité exponentielle. Ce travail se divise en trois parties. L'objectif de la première partie est de caractériser le défaut de compacité de l'injection de Sobolev de $H^2_{rad}(R^4)$ dans l'espace d'Orlicz $mathcal{L}(R^4)$.Le but de la deuxième partie est double : tout d'abord, on a décrit le défaut de compacité de l'injection de Sobolev de $H^1(R^2)$ dans les différentes classes d'espaces d'Orlicz, ensuite on a étudié une famille d'équations de Klein-Gordon non linéaires à croissance exponentielle. Cette étude inclut à la fois les problèmes d'existence globale, de complétude asymptotique et d'étude qualitative pour le problème de Cauchy associé. La troisième partie est dédiée à l'analyse des solutions de l'équation de Klein-Gordon 2D issues d'une suite de données de Cauchy bornée dans $H^1_{rad}(R^2)times L^2_{rad}(R^2)$. Basée sur les décompositions en profils, cette analyse a été conduite dans le cadre de la norme d'OrliczIn this thesis, we focused on the one hand on the description of the lack of compactness of the critical Sobolev embedding into different classes of Orlicz spaces, and on the other hand on the study of the nonlinear Klein-Gordon equation with exponential nonlinearity. This work is divided into three parts. The aim of the first part is to characterize the lack of compactness of the Sobolev embedding of $H^2_{rad}(R^4)$ into the Orlicz space $mathcal{L}(R^4)$.The aim of the second part is twofold: firstly, we describe the lack of compactness of the Sobolev embedding of $H^1(R^2)$ into different classes of Orlicz spaces, secondly we investigate a family of nonlinear Klein-Gordon equations with exponential nonlinearity. This study includes both the global existence problem, the asymptotic completeness and the qualitative study for the associated Cauchy problem. The third part is dedicated to the analysis of the solutions to the 2D Klein-Gordon equation associated to a sequence of bounded Cauchy data in $H^1_{rad}(R^2)times L^2_{rad}(R^2)$. Based on the profile decompositions, this analysis was conducted in the framework of Orlicz norm
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Tomková, Iva. "PERLA Ústí nad Orlicí." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2016. http://www.nusl.cz/ntk/nusl-354977.
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The object of the study is urban planning - architectural design strategy of conversion and revitalization of the factory PEARL 01 in Usti nad Orlici. The area of the site is about 3 hectares, an area eight times larger than the actual main square in the town. Most of the land is owned by the city. Current status of the area does not match the aesthetic or functional demands placed on this space, which is intended for expansion of the city center, whose current capacity does not match the needs of even the size of the city. Textile industry and Perla itself played an important role in the history of the region and influenced the lives of most local citizens. Therefore, the proposal seeks to retain as much of the original structure as possivle and with them the charm and spirit of the original factory and its buildings. The area is cleaned up, breathes and becomes in the first time in history a part of the urban space, and not a big barrier in its center.
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Annová, Denisa. "PERLA Ústí nad Orlicí." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2016. http://www.nusl.cz/ntk/nusl-354956.
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The subject of the diploma thesis is to design reclamation of brownfield PERLA 01 in Ústí nad Orlicí. The construction program consists conversion of existing building to assembly hall, gallery, tourist centre, sheltered workshop, rentable space, office building. New building is Start up centre. The project design a character of public space and a new square.
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Vlček, Marek. "Vysokoškolská kolej Hradec Králové, nábřeží Orlice." Master's thesis, Vysoké učení technické v Brně. Fakulta architektury, 2019. http://www.nusl.cz/ntk/nusl-401803.
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The diploma project is resolving the possibilities of designing contemporary buildings into the historical context of city centre. The emphasis is aimed on urban integration of new volumes into the present city structure and its genius loci. The result of the design should be buildings with specific character and clear dispositions using quality materials. The area is located near the city centre of Hradec Králové and is defined by the streets Comenius, I.Herrmann and Hradecká. It is directly adjacent to the historic city center. In the middle of the area is flowing The Orlice River, which divides area into two separately designed zones, communicates with each other. The presence of the river is considered to be a distinctive urban-forming element that needs to be used and promoted in the city. One of the characteristics of the site is the poor state of public spaces, several significant barriers, whether moving, operational or visible and urban unconnected areas or unreasonable used areas and buildings. The surrounding of The Orlice River, flowing through the center of Hradec Králové, is from near future very important, but at the same time hard to handle. All three facts - the city center plot, the presence of the river, but also the neglected public spaces - leading this area rehabilitated, revitalized and made accessible to people.
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Livovská, Lucia. "Hotel při ČPP aréně v Hradci Králové, nábřeží Orlice." Master's thesis, Vysoké učení technické v Brně. Fakulta architektury, 2019. http://www.nusl.cz/ntk/nusl-401802.
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The diploma project is resolving the possibilities of designing contemporary buildings into the historical context of city centre. The emphasis is aimed on urban integration of new volumes into the present city structure and its genius loci. The result of the design should be buildings with specific character and clear dispositions using quality materials. The area is located near the city centre of Hradec Králové and is defined by the streets Comenius, I.Herrmann and Hradecká. It is directly adjacent to the historic city center. In the middle of the area is flowing The Orlice River, which divides area into two separately designed zones, which is communicating with each other. The presence of the river is considered to be a distinctive urban-forming element that needs to be used and promoted in the city. One of the characteristics of the site is the poor state of public spaces, several significant barriers, whether moving, operational or visible and urban unconnected areas or unreasonable used areas and buildings. The surrounding of The Orlice River, flowing through the center of Hradec Králové, is from near future very important, but at the same time hard to handle. All three facts - the city center plot, the presence of the river, but also the neglected public spaces - leading this area rehabilitated, revitalized and made accessible to people.
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Charpentier, Stéphane. "Opérateurs de composition sur les espaces de fonctions holomorphes de plusieurs variables complexes : universalité dans les espaces de Banach et de Fréchet." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14104/document.
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Dans la première partie de ma thèse, il est démontré, dans les espaces de Banach et de Fréchet de suites, un résultat d'existence d'un sous-espace fermé de dimension infinie dont les éléments non-nuls sont des séries universelles.La deuxième partie est consacrée à l'étude des opérateurs de composition sur des espaces de fonctions holomorphes de plusieurs variables complexes. Dans un premier temps, le spectre et la dynamique des opérateurs de composition hyperboliques sur les espaces de Hardy de la boule sont décrits complètement.Dans un second temps, la continuité et la compacité des opérateurs de composition sur les espaces de Hardy-Orlicz et de Bergman-Orlicz de la boule sont caractérisées. On en déduit en particulier l'existence d'une classe de fonctions d'Orlicz définissant des espaces du type précédent sur lesquels tout opérateur de composition est continuIn the first part of my thesis, a result on the existence of a closed infinite-dimensional subspace, whose non-zero elements are universal series, is given in Banach and Fréchet spaces framework.The second part is devoted to the study of composition operators on spaces of several variables analytic functions. First, the spectrum and the dynamics of hyperbolic composition operators acting on Hardy spaces on the ball are completely described.Second, continuity and compactness of composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball are characterized. In particular, we deduce from the treatment of the continuity that there exists a class of Orlicz functions which define Hardy-Orlicz and Bergman-Orlicz spaces, on which every composition operator is bounded
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SONG, YUKUN SONG. "Stochastic Integrals with Respect to Tempered $\alpha$-Stable Levy Process." Case Western Reserve University School of Graduate Studies / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=case1501506513936836.
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Ghawadrah, Ghadeer. "Théorie descriptive des ensembles et espaces de Banach." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066078/document.
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Cette thèse traite de la théorie descriptive des ensembles et de la géométrie des espaces de Banach. La première partie consiste en l’étude de la complexité descriptive de la famille des espaces de Banach avec la propriété d’approximation bornée, respectivement la propriété π, dans l’ensemble des sous-espaces fermés de C(Δ), où Δ est l’ensemble de Cantor. Ces familles sont boréliennes. En outre, nous montrons que si alphaThis thesis deals with the descriptive set theory and the geometry of Banach spaces.The first chapter consists of the study of the descriptive complexity of the set of Banachspaces with the Bounded Approximation Property, respectively π-property, in the set ofall closed subspaces of C(∆), where ∆ is the Cantor set. We show that these sets areBorel. In addition, we show that if α<ω_1, the set of spaces with Szlenk index at most α which have a shrinking FDD is Borel. We show in the second chapter that the numberof isomorphism classes of complemented subspaces of the reflexive Orlicz function space L^Φ [0,1] is uncountable, where L^Φ [0,1]is not isomorphic to L^2 [0,1]
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Issa, Samar. "Méthodes variationnelles : Applications à l'analyse d'image et au modèle de Frenkel-Kontorova." Phd thesis, Université de La Rochelle, 2011. http://tel.archives-ouvertes.fr/tel-00808646.
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Cette thèse est décomposée en deux parties. La première est consacrée à l'étude de la restauration d'image et la seconde partie est consacrée à l'étude d'un modèle de Frenkel-Kontorova par des méthodes issues du calcul variationnel et des équations aux dérivées partielles. Au chapitre 1, nous présentons les questions essentielles que nous traiterons dans cette thèse, puis on fait des rappels sur les définitions et quelques propriétés d'espace des fonctions à variations bornées BV , l'espace d'Orlicz et le modèle de Frenkel-Kontorova. Au chapitre 2, nous montrons que les problèmes de minimisation non convexe (restauration d'image) contenant des termes de régularisation sous-linéaires sont mal posés. Au chapitre 3, nous étudions un modèle de restauration avec un terme de régularisation à croissance non standard, proposé par Blomgren et al. : le module du gradient est élevé a une puissance qui dépend elle même du gradient. On montre qu'elle est semi-continue inférieurement pour la topologie faible d'un certain espace d'Orlicz-Sobolev qui lui est associé, ce qui permet un résultat d'existence de la solution. Au chapitre 4, nous étudions un modèle de Frenkel-Kontorova, dont on montre l'existence d'au moins une solution de type travelling wave, u.
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Giri, Chinmay Kumar. "Orlicz Function Spaces and Composition Operator." Thesis, 2013. http://ethesis.nitrkl.ac.in/5436/1/411MA2075.pdf.
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In our dissertation we present here the salient features from the theory of Orlicz function spaces, LÖ(Ù), generated by the Young’s function Ö on an arbitrary ó−finite measurable spaces Ù. We will discussed these are the Banach spaces equipped with the equivalent orlicz and gauge norms.Finally we study the Composition operators Cô between Orlicz spaces LÖ(Ù) generated by measurable and non-singular transformations ô from Ù into itself. We also investigate the Boundedness and compactness of the composition operators on the Orlicz spaces by using different types of Ä2 conditions of the orlicz function Ö.
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Teymurazyan, Rafayel. "Obstacle type problems in Orlicz-Sobolev spaces." Doctoral thesis, 2013. http://hdl.handle.net/10451/8648.
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Tese de doutoramento, Matemática (Física Matemática e Mecânica dos Meios Contínuos), Universidade de Lisboa, Faculdade de Ciências, 2013This thesis consists of four chapters. In the first chapter we study the regularity of solutions for a class of elliptic problems in Orlicz-Sobolev spaces. In particular, we see that bounded weak solutions of Au := div a(x; jruj)ru _ = f(x); x 2 ; where Ω ⊂ Rn is a bounded domain, for an appropriate a and f are C1 α regular. Using Lewy-Stampacchia inequalities for one obstacle problem we derive C1 α regularity results (both locally and up to the boundary) for the solution of a quasilinear obstacle problem. In the second chapter we prove Lewy-Stampacchia inequalities in abstract form for two obstacles problem and for N-membranes problem. Applying those inequalities we derive C1 α regularity results (both locally and up to the boundary) for A(x)-obstacle problem with two obstacles and for N-membranes problem. As another application of Lewy-Stampacchia inequalities, we study a quasivariational problem related to a stochastic switching game. We prove, that the problem admits at least a maximal and a minimal solution. In the third chapter we extend the regularity of the free boundary of the obstacle problem to a class of heterogeneous quasilinear degenerate elliptic operators (including p(x)-Laplacian). We prove that the free boundary is a porous set and hence has Lebesgue measure zero. We also show that the (n - 1)-dimensional Hausdorff measure of the free boundary is finite (for p(x) > 2), which yields, in particular, that up to a negligible singular set, the free boundary is the union of at most a countable family of C1 hypersurfaces. Finally, in the chapter four of the thesis, after homogenizing the Dirichlet problem for A(x)-Laplacian in Orlicz-Sobolev spaces, we study the homogenization of the A(x)-obstacle problem, then prove convergence of the coincidence sets.
Fundação para a Ciência e a Tecnologia (FCT, SFRH/BD/40819/2007)
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Offwood, Theresa Maria. "No free lunch and risk measures on Orlicz spaces." Thesis, 2012. http://hdl.handle.net/10539/11942.
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The importance of Orlicz spaces in the study of mathematics of nance came
to the for in the 2000's when Frittelli and his collaborators connected the
theory of utility functions to Orlicz spaces. In this thesis, we look at how
Orlicz spaces play a role in nancial mathematics. After giving an overview of
scalar-valued Orlicz spaces, we look at the rst fundamental theorem of asset
pricing in an Orlicz space setting. We then give a brief summary of scalar risk
measures, followed by the representation result for convex risk measures on
Orlicz hearts. As an example of a risk measure, we take a detailed look at the
Wang transform both as a pricing mechanism and as a risk measure. As the
theory of nancial mathematics is moving towards the set-valued setting, we
give a description of vector-valued Orlicz hearts and their duals using tensor
products. Lastly, we look at set-valued risk measures on Orlicz hearts, proving
a robust representation theorem via a tensor product approach.
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Wróblewska-Kamińska, Aneta. "An application of Orlicz spaces in partial differential equations." Doctoral thesis, 2012. http://depotuw.ceon.pl/handle/item/138.
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Our purpose is to investigate mathematical properties of some systems of nonlinear partial differential equations where the nonlinear term is monotone and its behaviour - coercivity/growth conditions are given with the help of some general convex function defining Orlicz spaces.
Our first result is the existence of weak solutions to unsteady flows of non-Newtonian incompressible nonhomogeneous (with non-constant density) fluids with nonstandard growth conditions of the stress tensor. We are motivated by the problem of anisotropic behaviour of fluids which are also characterised by rapid shear thickness. Since we are interested in flows with the rheology more general than power-law-type, we describe the growth conditions with the help of an x–dependent convex function and formulate our problem in generalized Orlicz (Musielak-Orlicz) spaces.
As a second result we give a proof of the existence of weak solutions to the problem of the motion of one or several nonhomogenous rigid bodies immersed in a homogenous non-Newtonian fluid. The nonlinear viscous term in the equation is described with the help of a general convex function defining isotropic Orlicz spaces. The main ingredient of the proof is convergence of the nonlinear term achieved with the help of the pressure localisation method.
The third result concerns the existence of weak solutions to the generalized Stokes system with the nonlinear term having growth conditions prescribed by an anisotropic N -function. Our main interest is directed to relaxing the assumptions on the N- function and in particular to capture the shear thinning fluids with rheology close to linear. Additionally, for the purpose of the existence proof, a version of the Sobolev-Korn inequality in Orlicz spaces is proved.
Last but not least, we study also a general class of nonlinear elliptic problems, where the given right-hand side belongs only to the L1 space. Moreover the vector field is monotone with respect to the second variable and satisfies a non-standard growth condition described by an x-dependent convex function that generalizes both Lp(x) and classical Orlicz settings. Using truncation techniques and a generalized Minty method in the functional setting of non reflexive spaces we prove existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established. Sufficient conditions are specified which guarantee that the renormalized solution is already a weak solution to the problem.
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Zecca, Gabriella. "On the L^p-solvability of the Dirichlet problem and generalizations in Orlicz spaces." Tesi di dottorato, 2008. http://www.fedoa.unina.it/3509/1/tesiGZecca.pdf.
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Dhara, Raj Narayan. "Existence and regularity theory in weighted Sobolev spaces and applications." Doctoral thesis, 2016. https://depotuw.ceon.pl/handle/item/2051.
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In the thesis we discuss several questions related to the study of degenerate, possibly nonlinear PDEs of elliptic type. At first we discuss the equivalent conditions between the validity of weighted Poincar\'e inequalities, structure of the functionals on weighted Sobolev spaces, isoperimetric inequalities and the existence and uniqueness of solutions to the degenerate nonlinear elliptic PDEs with nonhomogeneous boundary condition, having the form:\begin{eqnarray}\label{eqn:abs}\left\{\begin{array}{lll}{\rm div} \left( \rho (x)|\nabla u|^{p-2}\nabla u\right) =x^*,\\~~~~~~~~~~~~u-w \in W^{1,p}_{\rho,0} (\Omega),\end{array}\right.\end{eqnarray}involving any given $x^*\in (W^{1,p}_{\rho,0} (\Omega))^*$ and $w\in W^{1,p}_{\rho} (\Omega)$, where $u\in W^{1,p}_{\rho} (\Omega)$ and $W^{1,p}_{\rho} (\Omega)$ denotes certain weighted Sobolev space, $W^{1,p}_{\rho,0} (\Omega)$ is the completion of $\mathcal{C}_{0}^{\infty}(\Omega)$. As a next step, we undertake a natural question how to interpret the nonhomogenous boundary conditions in weighted Sobolev spaces, when the natural analytical tools, like trace embedding theorems, are missing. Our further goal is to contribute to solvability and uniqueness for degenerate elliptic PDEs with nonhomogenous boundary condition being the extension of~\eqref{eqn:abs}. In addition to the monotonicity method used in the first step of our discussion for the problem~\eqref{eqn:abs}, we also exploit Lax-Miligram theorem to treat the linear problem like:\begin{equation*}\begin{cases}-{\rm div} (A(x)\nabla u(x)) + B(x)\cdot\nabla u(x) + C(x)u(x) = x^{*}\ \ \text{for a.e.}\ x\in \Omega, \\~~~~~~~~~~~~~~~~~~ u(x) = g(x) \ \ \text{for a.e. }\ x\in \partial\Omega ,\end{cases}\end{equation*}as well as Ekeland's Variational Principle and Boccardo-Murat techniques to consider problem like:\begin{align*} \begin{cases} - {\rm div} \left( \rho (x)|\nabla u|^{p-2}\nabla u\right) - \lambda\, b(x)| u|^{p-2} u = x^*,\\~~~~~~~~~~~~~~~~~~~u-z \in X , \end{cases}\end{align*}where $p>1,\ \lambda>0$, and the operator $\mathcal{L}_{\lambda} u:= - {\rm div} \left( \rho (x)|\nabla u|^{p-2}\nabla u\right) - \lambda\, b(x)| u|^{p-2} u $ is non-monotone.For the study of the nonhomogeneous BVPs, we apply recent results due to Ka\l{}amajska and myself, where we constructed trace extension operator from weighted Orlicz-Slobodetskii spaces defined on the boundary of the domain to weighted Orlicz-Sobolev spaces in the domain. Information on the spectrum of the corresponding differential operator is also derived. Moreover, some nonexistence and nonuniqueness results are also analyzed.
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El-Mabrouk, Khalifa [Verfasser]. "Semilinear perturbations of harmonic spaces and Martin-Orlicz capacities : an approach to the trace of moderate U-functions / vorgelegt von Khalifa El Mabrouk." 2002. http://d-nb.info/964456435/34.
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Buriánková, Eva. "Chování jednorozměrných integrálních operátorů na prostorech funkcí." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-346973.
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In this manuscript we study the action of one-dimensional integral operators on rearrangement-invariant Banach function spaces. Our principal goal is to characterize optimal target and optimal domain spaces corresponding to given spaces within the category of rearrangement-invariant Banach function spaces as well as to establish pointwise estimates of the non-increasing rearrangement of a given operator applied on a given function. We apply these general results to proving optimality relations between special rearrangement-invariant spaces. We pay special attention to the Laplace transform, which is a pivotal example of the operators in question. Powered by TCPDF (www.tcpdf.org)
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Naik, S. "Multipliers between Orlicz sequence space." Thesis, 2014. http://ethesis.nitrkl.ac.in/6292/1/E-74.pdf.
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Let $ M,N $ be Orlicz functions and let $ D(l_M,l_N) $ be the space of all diagonal operators (that is multipliers) acting between the Orlicz sequence spaces $ l_M $ and $ l_N $. We prove that the space of multipliers $ D(l_M,l_N) $ coincides with (and is isommorphic to) the Orlicz sequence space $ l_{M_{N}^*} $, where $ M_{N}^* $ is the Orlicz function defined by $ M_N^*( \lambda )=\text{sup} \lbrace N( \lambda x)-M(x),x\in(0,1) \rbrace $ .
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Skrzypczak, Iwona. "Hardy–type inequalities and nonlinear eigenvalue problems." Doctoral thesis, 2013.
Find full textAbstract:
Naszym celem jest wprowadzenie nowej metody konstruowania nier´owno´sci
typu Hardy’ego. Konstruujemy je znaj¸ac rozwi¸azania u zagadnie´n p oraz A–
harmonicznych. Wyprowadzamy nier´owno´sci typu Caccioppoli dla u. Jako
wniosek z nich otrzymujemy wa˙zone nier´owno´sci typu Hardy’ego dla funkcji
Lipschitzowskich o zwartym no´sniku.
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Skříšovský, Emil. "Stlačitelné Navier-Stokes-Fourierovy rovnice pro adiabatický koeficient blízko jedničky." Master's thesis, 2019. http://www.nusl.cz/ntk/nusl-405891.
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In the present thesis we study the compressible Navier-Stokes-Fourier sys- tem. This is a system of partial differential equations describing the evolutionary problem for an adiabatic flow of a heat conducting compressible viscous fluid in a bounded domain. Here we consider the problem in two dimensions with zero Dirichlet boundary conditions for velocity. The cold pressure term in the pressure law for the momentum equation is here considered in the form pC(ϱ) ∼ ϱ logα (1+ϱ) for some α > 0, for which we need to work on the scale of Orlicz spaces in order to obtain useful estimates and in those space we formulate the problem weakly and also establish the weak compactness of the solution. The main result of this thesis is Theorem 6.1 where we show the existence of a weak solution with no assumptions on the size of the data and on arbitrary large time intervals. 1
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Kleprlík, Luděk. "Vlastnosti slabě diferencovatelných funkcí a zobrazení." Doctoral thesis, 2014. http://www.nusl.cz/ntk/nusl-342351.
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We study the optimal conditions on a homeomorphism f : Ω → Rn which guarantee that the composition u◦f is weakly differentiable and its weak derivative belongs to the some function space. We show that if f has finite distortion and q-distortion Kq = |Df|q /Jf is integrable enough, then the composition operator Tf (u) = u ◦ f maps functions from W1,q loc into space W1,p loc and the well-known chain rule holds. To prove it we characterize when the inverse mapping f−1 maps sets of measure zero onto sets of measure zero (satisfies the Luzin (N−1 ) con- dition). We also fully characterize conditions for Sobolev-Lorentz space WLn,q for arbitrary q and for Sobolev Orlicz space WLq log L for q ≥ n and α > 0 or 1 < q ≤ n and α < 0. We find a necessary condition on f for Sobolev rearrangement invariant function space WX close to WLq , i.e. X has q-scaling property. 1
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Zindulka, Mikuláš. "Bázové posloupnosti v Banachových prostorech." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448170.
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An ordering on bases in Banach spaces is defined as a natural generalization of the notion of equivalence. Its theory is developed with emphasis on its behavior with respect to shrinking and boundedly-complete bases. We prove that a bounded operator mapping a shrinking basis to a boundedly-complete one is weakly compact. A well-known result concerning the factorization of a weakly compact operator through a reflexive space is then reinterpreted in terms of the ordering. Next, we introduce a class of Banach spaces whose norm is constructed from a given two-dimensional norm N. We prove that any such space XN is isomorphic to an Orlicz sequence space. A key step in obtaining this correspondence is to describe the unit circle in the norm N with a convex function ϕ. The canonical unit vectors form a basis of a subspace YN of XN . We characterize the equivalence of these bases and the situation when the basis is boundedly-complete. The criteria are formulated in terms of the norm N and the function ϕ. 1
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Takáč, Jakub. "Interpolace logaritmicky konvexních kombinací operátorů." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448302.
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We study the behaviour of logarithmically convex combinations of operators given by Tf = |S1f| 1 θ |S2f|1− 1 θ , where S1, S2 are some (usually quasi-linear) operators acting on spaces of measurable functions and θ ∈ (1, ∞) is a parameter. We develop two, quite different in nature, interpolation theories, each of which enables us to obtain a rather com- prehensive information about the behavior of such operators on function spaces. The first one is completely general and is based on abstract interpolation and Calderón spaces. We illustrate the theoretical results by a wide variety of examples of pairs of spaces X, Y such that T: X → Y is bounded, these in particular include the so-called Calderón-Lozanovskiı̌ construction. The second theory departs from pointwise estimates by Calderón operators and is particularly tailored for obtaining boundedness results between Orlicz spaces given weak-type estimates that arise in applications. A common feature of both theories is an approach, apparently new, involving interpolation of four spaces. The input data in each case consists of two reasonable separate endpoint estimates for the operators S1 and S2. 1
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Klawe, Filip. "Mathematical analysis of thermo-visco-elastic models." Doctoral thesis, 2015.
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Our research is directed to quasi-static evolution of thermo-visco-elastic models. We assume that the material is subject to two kinds of mechanical deformations: elastic and inelastic. Moreover, our analysis captures the influence of the temperature on visco-elastic properties of the body. The subject of this dissertation is to study a thermodynamically consistent models which describe such type of phenomena related to Mróz model, Norton-Hoff-type model and model with growth conditions in Orlicz spaces. The proofs base on two level Galerkin approximation. We present the construction of approximate solutions and discuss their existence. Moreover, the problem of low data regularity in parabolic equation appears for considered models. The paper presents two possible ways how to deal with it, i.e. the approach of Boccardo & Gallouet and the approach of renormalized solutions.We provide proofs regarding existence of solutions to thermo-visco-elastic models in a simplified setting, namely the thermal expansion effects are neglected. Consequently, the coupling between the temperature and the displacement occurs only in the constitutive function for the evolution of the visco-elastic strain.Nasze badania koncentrują się na analizie modeli termo-lepko-sprężystych opisujących ewolucję quasi-statyczną. Rozważamy modele, które łączą odkształcenia odwracalne (sprężyste) i nieodwracalne (lepko-sprężyste). Dodatkowo, pojawienie się w modelu odkształceń nieodwracalnych związane jest z dysypacją energii mechanicznej i pojawieniem się efektów cieplnych, które również są przedmiotem analizy.Przedmiotem badań prezentowanych w niniejszej pracy są modele termodynamicznie domknięte opisujące to zjawisko. Dowodzimy istnienia rozwiązań dla modelu Mroza, modelu typu Nortona-Hoffa i modelu z warunkami wzrostu w przestrzeniach Orlicza.Dowody istnienia rozwiązań oparte są na dwustopniowej aproksymacji Galerkina. Prezentujemy konstrukcję rozwiązań przybliżonych oraz dowodzimy ich istnienia. Ponadto, w rozważanych modelach pojawia się problem niskiej regularności danych w równaniu przewodnictwa cieplnego. Rozważamy dwa sposoby rozwiązania tego problemu, tj. podejście Boccardo & Galloueta oraz podejście oparte na teorii rozwiązań zrenormalizowanych.Dodatkowo zakładamy, że rozważane materiały nie ulegają rozszerzalności cieplnej. W związku z tym, zależność przemieszczenia i temperatury jest spowodowana tylko przez funkcję konstytutywną opisującą ewolucję tensora lepko-sprężystego.
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Musil, Vít. "Klasické operátory harmonické analýzy v Orliczových prostorech." Doctoral thesis, 2018. http://www.nusl.cz/ntk/nusl-392438.
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Classical operators of harmonic analysis in Orlicz spaces V'ıt Musil We deal with classical operators of harmonic analysis in Orlicz spaces such as the Hardy-Littlewood maximal operator, the Hardy-type integral operators, the maximal operator of fractional order, the Riesz potential, the Laplace transform, and also with Sobolev-type embeddings on open subsets of Rn or with respect to Frostman measures and, in particular, trace embeddings on the boundary. For each operator (in case of embeddings we consider the identity operator) we investigate the question of its boundedness from an Orlicz space into another. Particular attention is paid to the sharpness of the results. We further study the question of the existence of optimal Orlicz domain and target spaces and their description. The work consists of author's published and unpublished results compiled together with material appearing in the literature.
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Musil, Vít. "Poloha Orliczova prostoru a optimalita." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-340763.
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Given a rearrangement-invariant Banach function space Y (Ω), we consider the problem of the existence of an optimal (largest) domain Or- licz space LA (Ω) satisfying the Sobolev embedding Wm LA (Ω) !Y (Ω). We present a complete solution of this problem within the class of Marcinkiewicz endpoint spaces which covers several important examples.
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Le, Van Dinh. "The broken circuit complex and the Orlik - Terao algebra of a hyperplane arrangement." Doctoral thesis, 2016. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016021714257.
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My thesis is mostly concerned with algebraic and combinatorial aspects of the
theory of hyperplane arrangements. More specifically, I study the Orlik-Terao algebra of a hyperplane arrangement and the broken circuit complex of a matroid. The Orlik-Terao algebra is a useful tool for studying hyperplane arrangements, especially for characterizing some non-combinatorial properties. The broken circuit complex, on the one hand, is closely related to the Orlik-Terao algebra, and on the other hand, plays a crucial role in the study of many combinatorial problem: the coefficients of the characteristic polynomial of a matroid are encoded in the f-vector of the broken circuit complex of the matroid. Among main results of the thesis are characterizations of the complete intersection and Gorenstein properties of the broken circuit complex and the Orlik-Terao algebra. I also study the h-vector of the broken circuit complex of a series-parallel network and relate certain entries of that vector to ear decompositions of the network. An application of the Orlik-Terao algebra in studying the relation space of a hyperplane arrangement is also included in the thesis.