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Rozprawy doktorskie na temat „Calculus of variations”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Tavares, Dina dos Santos. "Fractional calculus of variations." Doctoral thesis, Universidade de Aveiro, 2017. http://hdl.handle.net/10773/22184.

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Doutoramento em Matemática e Aplicações<br>O cálculo de ordem não inteira, mais conhecido por cálculo fracionário, consiste numa generalização do cálculo integral e diferencial de ordem inteira. Esta tese é dedicada ao estudo de operadores fracionários com ordem variável e problemas variacionais específicos, envolvendo também operadores de ordem variável. Apresentamos uma nova ferramenta numérica para resolver equações diferenciais envolvendo derivadas de Caputo de ordem fracionária variável. Consideram- -se três operadores fracionários do tipo Caputo, e para cada um deles é apresentad

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2

Ferreira, Rui Alexandre Cardoso. "Calculus of variations on time scales and discrete fractional calculus." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/2921.

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Doutoramento em Matemática<br>Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fr

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3

Zhang, Chengdian. "Calculus of variations with multiple integration." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/20436929.html.

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4

Capet, SteÌphane. "Calculus of variations in quantum mechanics." Thesis, University of Warwick, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444831.

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5

Santos, Simão Pedro Silva. "Calculus of variations of Herglotz type." Doctoral thesis, Universidade de Aveiro, 2017. http://hdl.handle.net/10773/22503.

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Doutoramento em Matemática<br>We consider several problems based on Herglotz’s generalized variational problem. We dedicate two chapters to extensions on Herglotz’s generalized variational problem to higher-order and first-order problems with time delay, using a variational approach. In the last four chapters, we rewrite Herglotz's type problems in the optimal control form and use an optimal control approach. We prove generalized higher- order Euler-Lagrange equations, first without and then with time delay; higher-order natural boundary conditions; Noether's first theorem for the first-order

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6

Gratwick, Richard. "Singular minimizers in the calculus of variations." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/47653/.

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This thesis examines the possible failure of regularity for minimizers of onedimensional variational problems. The direct method of the calculus of variations gives rigorous assurance that minimizers exist, but necessarily admits the possibility that minimizers might not be smooth. Regularity theory seeks to assert some extra smoothness of minimizers. Tonelli's partial regularity theorem states that any absolutely continuous minimizer has a (possibly infinite) classical derivative everywhere, and this derivative is continuous as a function into the extended real line. We examine the limits of

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7

Taheri, Ali. "Local minimizers in the calculus of variations." Thesis, Heriot-Watt University, 1997. http://hdl.handle.net/10399/656.

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8

Perrotta, Stefania. "Some Problems in the Calculus of Variations." Doctoral thesis, SISSA, 1996. http://hdl.handle.net/20.500.11767/4452.

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9

Bedford, Stephen James. "Calculus of variations and its application to liquid crystals." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:a2004679-5644-485c-bd35-544448f53f6a.

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The thesis concerns the mathematical study of the calculus of variations and its application to liquid crystals. In the first chapter we examine vectorial problems in the calculus of variations with an additional pointwise constraint so that any admissible function <strong>n</strong> ε W<sup>1,1</sup>(ΩM), and M is a manifold of suitable regularity. We formulate necessary and sufficient conditions for any given state <strong>n</strong> to be a strong or weak local minimiser of I. This is achieved using a nearest point projection mapping in order to use the more classical results which apply in

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10

Chan, Ka-bo, and 陳家寶. "On Griffiths' formalism of the calculus of variations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30456630.

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11

Arora, Raman. "Analysis of Economic Models Through Calculus of Variations." TopSCHOLAR®, 2005. http://digitalcommons.wku.edu/theses/453.

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This thesis is a combination of two science fields: Mathematics and Economics. Mathematics is often used to formulate a clear and concise solution to economic problems. In my observation calculus of variation has often been used in various macroeconomic problems. This mathematical method deals with maximizing or minimizing of various objective functions given a set of constraints. This topic brings out one of the best ways to show the relationship between mathematics and economics. My thesis consists of three parts: The first chapter contains a review of the calculus of variations. Basic defin

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12

Campos, Cordero Judith. "Regularity and uniqueness in the calculus of variations." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:81e69dac-5ba2-4dc3-85bc-5d9017286f13.

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This thesis is about regularity and uniqueness of minimizers of integral functionals of the form F(u) := ∫Ω F(∇u(x)) dx; where F∈C2(RNn) is a strongly quasiconvex integrand with p-growth, Ω⊆RnRn is an open bounded domain and u∈W1,pg(Ω,RN) for some boundary datum g∈C1,α(‾Ω, RN). The first contribution of this work is a full regularity result, up to the boundary, for global minimizers of F provided that the boundary condition g satisfies that ΙΙ∇gΙΙLP < ε for some ε > 0 depending only on n;N, the parameters given by the strong quasiconvexity and p-growth conditions and, most importantly, on an a

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13

Chen, Chuei Yee. "Quasiminimality and coercivity in the calculus of variations." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d6daadfd-92fb-4fa6-9d5b-fd8403955079.

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14

Zagatti, Sandro. "Some Problems in the Calculus of the Variations." Doctoral thesis, SISSA, 1992. http://hdl.handle.net/20.500.11767/4226.

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15

Onofrei, Daniel T. "Homogenization of an elastic-plastic problem." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0430103-121632.

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16

Crasta, Graziano. "Nonconvex problems in Control Theory and Calculus of Variations." Doctoral thesis, SISSA, 1995. http://hdl.handle.net/20.500.11767/4503.

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17

Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, Università degli studi di Trento, 2010. https://hdl.handle.net/11572/368036.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on

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18

Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, University of Trento, 2010. http://eprints-phd.biblio.unitn.it/170/1/Constrained_Calculus_of_Variations_and_Geometric_Optimal_Control_Theory.pdf.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on

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19

Bellettini, Giovanni. "Geometric problems involving curvatures in the calculus of variations." Doctoral thesis, SISSA, 1993. http://hdl.handle.net/20.500.11767/4064.

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20

Chow, Hong-Yu, and 周康宇. "Griffiths' formalism of the calculus of variations and applications toinvariants." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35812503.

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21

Chow, Hong-Yu. "Griffiths' formalism of the calculus of variations and applications to invariants." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35812503.

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22

Kabisch, Sandra. "On established and new semiconvexities in the calculus of variations." Thesis, University of Surrey, 2016. http://epubs.surrey.ac.uk/812076/.

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After introducing the topics that will be covered in this work we review important concepts from the calculus of variations in elasticity theory. Subsequently the following three topics are discussed: The first originates from the work of Post and Sivaloganathan [\emph{Proceedings of the Royal Society of Edinburgh, Section: A Mathematics}, 127(03):595--614, 1997] in the form of two scenarios involving the twisting of the outer boundary of an annulus $A$ around the inner. It seeks minimisers of $∫_A \frac{1}{2}|∇u|^2 \d x$ among deformations $u$ with the constraint $\det ∇u ≥0$ a.e.~as well as

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23

Dodd, Thomas James. "Partial regularity of local minimisers in the calculus of variations." Thesis, Heriot-Watt University, 2010. http://hdl.handle.net/10399/2404.

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24

Dryl, Monika. "Calculus of variations on time scales and applications to economics." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/12869.

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Doutoramento em Matemática<br>We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus ar

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25

Crispin, Daniel John. "Brake periodic orbits and linking in the calculus of variations." Thesis, University of Bath, 2004. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410925.

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26

Varvaruca, Lorina. "Singular minimizers in the calculus of variations and nonlinear elasticity." Thesis, University of Bath, 2007. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.439277.

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27

Celada, Pietro. "Some Scalar and Vectorial Problems in the Calculus of Variations." Doctoral thesis, SISSA, 1997. http://hdl.handle.net/20.500.11767/4349.

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28

BONFANTI, GIOVANNI. "Progresses on some classical problems of the calculus of variations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/28223.

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Some theorems about the validity of the Euler-Lagrange equation are proved. In particular, Lagrangians without regularity hypothesis or without growth assumptions are considered. Moreover, a result about the non-occurrence of the Lavrentiev phenomenon in the scalar case is proved.

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29

Hopper, Christopher Peter. "On the regularity of holonomically constrained minimisers in the calculus of variations." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:d8bde7a2-7dae-44d2-919d-48b9f2543789.

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This thesis concerns the regularity of holonomic minimisers of variational integrals in the context of direct methods in the calculus of variations. Specifically, we consider Sobolev mappings from a bounded domain into a connected compact Riemannian manifold without boundary, to which such mappings are said to be holonomically constrained. For a general class of strictly quasiconvex integral functionals, we give a direct proof of local C<sup>1,α</sup>-Hölder continuity, for some 0 < α < 1, of holonomic minimisers off a relatively closed 'singular set' of Lebesgue measure zero. Cru

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30

Iqbal, Zamin. "Variational methods in solid mechanics." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301901.

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31

Muller, Stefan. "Variational problems in mechanics and analysis." Thesis, Heriot-Watt University, 1989. http://hdl.handle.net/10399/925.

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32

Bandeira, Luís Miguel Zorro. "Analysis of new situations for quasiconvexity versus rank-one convexity in 2 x 2 and other dimensions." Doctoral thesis, Universidade de Évora, 2008. http://hdl.handle.net/10174/11119.

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It is well-known that quasiconvexity is a fundamental concept for vector problems in the Calculus of Variations. Its main necessary condition is rankone convexity. Still today it is not known whether it is also sufficient or not, when the target space of deformations is m=2 (in the general case). We introduce a method to find, in a systematic way, rank-one convex polynomials. We show how it works in several examples. It can also be applied to convexity along general cones. An alternative proof is provided for the well-known quadratic case of quasiconvexity, which does not use the Plancherel fo

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33

McMahon, Chris. "Calculus of Variations on Time Scales and Its Applications to Economics." TopSCHOLAR®, 2008. http://digitalcommons.wku.edu/theses/370.

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The goal of time scale research is to progress the development of a harmonized theory that is all encompassing of the more commonly known specialized forms. The main results of this paper is the presentation of the Ramsey model which can be written using both the A and V operators, and solved using the two separate theories of the calculus of variations on time scales. The next presentation will be of the solution of an adjustment model, for a specific form of a time scale, whose functional can only be optimized, using the existing theory, when written with the A operator. We will also develop

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34

Bevan, Jonathan. "Polyconvexity and counterexamples to regularity in the multidimensional calculus of variations." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275363.

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35

Pooseh, Shakoor. "Computational methods in the fractional calculus of variations and optimal control." Doctoral thesis, Universidade de Aveiro, 2013. http://hdl.handle.net/10773/11510.

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Doutoramento em Matemática<br>The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their effi

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36

Saunders, D. J. "The geometry of jet bundles, with applications to the calculus of variations." Thesis, Open University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376035.

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37

Fanzon, Silvio. "Geometric patterns and microstructures in the study of material defects and composites." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/72566/.

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The main focus of this PhD thesis is the study of microstructures and geometric patterns in materials, in the framework of the Calculus of Variations. My PhD research, carried out in collaboration with my supervisor Mariapia Palombaro and Marcello Ponsiglione, led to the production of three papers [21, 22, 23]. Papers [21, 22] have already been published, while [23] is currently in preparation. This thesis is divided into two main parts. In the first part we present the results obtained in [22, 23]. In these two works geometric patterns have to be understood as patterns of dislocations in crys

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38

Morrison, George. "Rotationally-symmetric solutions to a nonlinear elliptic system under an incompressibility constraint and related problems." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/79856/.

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39

Christopher, Jason W. "Using calculus of variations to optimize paths of descent through ski race courses." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32840.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.<br>Includes bibliographical references (p. 69-70).<br>The goal of ski racing is to pass through a series of gates as quickly as possible. There are many paths from gate to gate, but there is only one path that is fastest. By knowing what the fastest path is, a racer could shave tenths of seconds off his or her time. That is a tremendous amount of time considering that races are won by hundredths of a second. This thesis attempts to calculate the fastest path through a ski race course using several simplifications suc

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40

Buß, Hinderk M. "A posteriori error estimators based on duality techniques from the calculus of variations." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10790752.

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41

Fordred, Gordon Ian. "An application of the Malliavin calculus in finance." Diss., Pretoria : [s.n.], 2009. http://upetd.up.ac/thesis/available/etd-07062009-123751.

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42

Chen, Pei-Tai. "Axisymmetric vibration, acoustic radiation, and the influence of eigenvalue veering phenomena in prolate spheroidal shells using variational principles." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/19407.

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43

黃志榮 and Chi-wing Wong. "On Cartan form and equivalence of variational problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31220071.

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44

Lauteri, Gianluca. "The Emergence of Cosserat-type Structures in Metal Plasticity." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-225513.

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We study an energy functional able to describe low energy configurations of a two dimensional lattice with dislocations in a nonlinear elasticity regime. The main result can be described as follows: configurations of energy comparable to the lattice spacing consist of piecewise constant microrotations with small angle grain boundaries between them. Moreover, we also give bounds to the energy of particular configurations describing a small angle symmetric tilt grain boundary.

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45

Wong, Chi-wing. "On Cartan form and equivalence of variational problems /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19472602.

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46

Morris, Charles Graham. "Mapping problems in the calculus of variations : twists, L1-local minimisers and vectorial symmetrisation." Thesis, University of Sussex, 2017. http://sro.sussex.ac.uk/id/eprint/72567/.

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47

Khodadadi, Mohammad. "Exploration of variations of unrestricted blocking for description logics." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/exploration-of-variations-of-unrestricted-blocking-for-description-logics(3fc15638-1483-42d0-a827-75cb231f0737).html.

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Description logics are a family of logics that provide formalisms for representing and reasoning about knowledge, based on describing concepts, in a structured and formally well-understood way. They provide the logical foundation for the web ontology language (OWL), which increased awareness of them recently. The most popular techniques for decision procedures for description logics are tableau reasoning methods, which have a long tradition and are well established in automated reasoning. This thesis investigates the possibility of finding a general and optimised blocking mechanism for descrip

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48

Turski, Jacek. "Calculus of variations for discontinous fields and its applications to selected topics in continuum mechanics." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72804.

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49

Bourdin, Loïc. "Contributions au calcul des variations et au principe du maximum de Pontryagin en calculs time scale et fractionnaire." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3009/document.

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Cette thèse est une contribution au calcul des variations et à la théorie du contrôle optimal dans les cadres discret, plus généralement time scale, et fractionnaire. Ces deux domaines ont récemment connu un développement considérable dû pour l’un à son application en informatique et pour l’autre à son essor dans des problèmes physiques de diffusion anormale. Que ce soit dans le cadre time scale ou dans le cadre fractionnaire, nos objectifs sont de : a) développer un calcul des variations et étendre quelques résultats classiques (voir plus bas); b) établir un principe du maximum de Pontryagin

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50

Botelho, Fabio Silva. "Variational Convex Analysis." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/28351.

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This work develops theoretical and applied results for variational convex analysis. First we present the basic tools of analysis necessary to develop the core theory and applications. New results concerning duality principles for systems originally modeled by non-linear differential equations are shown in chapters 9 to 17. A key aspect of this work is that although the original problems are non-linear with corresponding non-convex variational formulations, the dual formulations obtained are almost always concave and amenable to numerical computations. When the primal problem has no solution in

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