Relevant bibliographies by topics / Degenerate elliptic equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Degenerate elliptic equation'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Degenerate elliptic equation"

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Trudinger, Neil S. "On degenerate fully nonlinear elliptic equations in balls." Bulletin of the Australian Mathematical Society 35, no. 2 (April 1987): 299–307. http://dx.doi.org/10.1017/s0004972700013253.

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We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.
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Igisinov, S. Zh, L. D. Zhumaliyeva, A. O. Suleimbekova, and Ye N. Bayandiyev. "Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 107, no. 3 (September 30, 2022): 51–58. http://dx.doi.org/10.31489/2022m3/51-58.

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In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure the existence and uniqueness of the solution. The existence, uniqueness, and smoothness of a solution are proved, and estimates are found for singular numbers (s-numbers) and eigenvalues of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration.
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Le, Nam Q. "On the Harnack inequality for degenerate and singular elliptic equations with unbounded lower order terms via sliding paraboloids." Communications in Contemporary Mathematics 20, no. 01 (October 23, 2017): 1750012. http://dx.doi.org/10.1142/s0219199717500122.

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We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized Monge–Ampère equations. Our argument allows us to prove the doubling estimate for functions which, at points of large gradient, are solutions of (degenerate and singular) elliptic equations with unbounded drift.
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Tanirbergen, Aisulu K. "A MIXED PROBLEM FOR A DEGENERATE MULTIDIMENSIONAL ELLIPTIC EQUATION." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 3 (211) (September 30, 2021): 37–41. http://dx.doi.org/10.18522/1026-2237-2021-3-37-41.

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This article shows the unique solvability and obtains an explicit form of the classical solution of the mixed prob-lem in a cylindrical domain for a model degenerate multidimensional elliptic equation. The correctness of boundary value problems in the plane for elliptic equations by the method of the theory of ana-lytic functions of a complex variable has been well studied. The first boundary value problem or the Dirichlet problem for multidimensional elliptic equations with degeneration on the boundary has been sufficiently analyzed. However, as we know, the mixed problem for the indicated equations has been studied very little.
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Andreu, F., V. Caselles, and J. M. Mazón. "A strongly degenerate quasilinear elliptic equation." Nonlinear Analysis: Theory, Methods & Applications 61, no. 4 (May 2005): 637–69. http://dx.doi.org/10.1016/j.na.2004.11.020.

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Krasovitskii, T. I. "Degenerate elliptic equations and nonuniqueness of solutions to the Kolmogorov equation." Доклады Академии наук 487, no. 4 (August 27, 2019): 361–64. http://dx.doi.org/10.31857/s0869-56524874361-364.

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In this paper we propose a new method of constructing examples of nonuniqueness of probability solutions by reducing the stationary Fokker-Planck-Kolmogorov equation to a degenerate elliptic equation on a bounded domain.
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Rocca, Elisabetta, and Riccarda Rossi. "A degenerating PDE system for phase transitions and damage." Mathematical Models and Methods in Applied Sciences 24, no. 07 (April 14, 2014): 1265–341. http://dx.doi.org/10.1142/s021820251450002x.

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In this paper, we analyze a PDE system arising in the modeling of phase transition and damage phenomena in thermoviscoelastic materials. The resulting evolution equations in the unknowns ϑ (absolute temperature), u (displacement), and χ (phase/damage parameter) are strongly nonlinearly coupled. Moreover, the momentum equation for u contains χ-dependent elliptic operators, which degenerate at the pure phases (corresponding to the values χ = 0 and χ = 1), making the whole system degenerate. That is why, we have to resort to a suitable weak solvability notion for the analysis of the problem: it consists of the weak formulations of the heat and momentum equation, and, for the phase/damage parameter χ, of a generalization of the principle of virtual powers, partially mutuated from the theory of rate-independent damage processes. To prove an existence result for this weak formulation, an approximating problem is introduced, where the elliptic degeneracy of the displacement equation is ruled out: in the framework of damage models, this corresponds to allowing for partial damage only. For such an approximate system, global-in-time existence and well-posedness results are established in various cases. Then, the passage to the limit to the degenerate system is performed via suitable variational techniques.
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Gutiérrez, Cristian E., and Federico Tournier. "Harnack Inequality for a Degenerate Elliptic Equation." Communications in Partial Differential Equations 36, no. 12 (December 2011): 2103–16. http://dx.doi.org/10.1080/03605302.2011.618210.

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Horiuchi, Toshio. "Quasilinear degenerate elliptic equation with absorption term." Nonlinear Analysis: Theory, Methods & Applications 47, no. 3 (August 2001): 1649–57. http://dx.doi.org/10.1016/s0362-546x(01)00298-x.

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Amano, Kazuo. "The Dirichlet problem for degenerate elliptic 2-dimensional Monge-Ampère equation." Bulletin of the Australian Mathematical Society 37, no. 3 (June 1988): 389–410. http://dx.doi.org/10.1017/s0004972700027015.

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We study the following Dirichlet problem for the degenerate elliptic Monge-Ampère equation: Given , f ≥ 0 and , find a solution , t ≥ 2, satisfying in Ω and u = g on ∂Ω. Since f is nonnegative, we cannot apply any standard elliptic methods. In this paper, we use an iteration scheme of Nash-Moser type and a priori estimates for degenerate elliptic operators, and solve the Dirichlet problem for a certain class of f and g.
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Dissertations / Theses on the topic "Degenerate elliptic equation"

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ROCCHETTI, DARIO. "Generation of analytic semigroups for a class of degenerate elliptic operators." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/749.

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Questa tesi è suddivisa in due capitoli. Nel primo si da un risultato di buona positura per una classe di problemi parabolici degeneri. I risultati ottenuti, validi in dimensione 2, garantiscono che le soluzioni di tali problemi supportano l'integrazione per parti. Nel secondo capitolo, si studia la controllabilità allo zero per una classe di operatori parabolici degeneri in forma non-divergenza. In particolare, i coefficienti del termine del secondo ordine possono degenerare al bordo del dominio spaziale. A questo scopo si giunge previo una disuguaglianza di osservabilità per il problema aggiunto usando opportune stime di Carleman.
This thesis is composed by two chapters. The first one is devoted to the generation of analytic semigroups in the L^2 topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimension, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type estimates for degenerate parabolic operators. In the second chapter we give null controllability results for some degenerate parabolic equations in non divergence form with a drift term in one space dimension. In particular, the coefficient of the second order term may degenerate at the extreme points of the space domain. For this purpose, we obtain an observability inequality for the adjoint problem using suitable Carleman estimates.
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GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.

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This thesis focuses on qualitative and quantitative aspects of some nonlinear PDEs arising in optimal control and differential games, ranging from regularity issues to maximum principles. More precisely, it is concerned with the analysis of some fully nonlinear second order degenerate PDEs over Hörmander vector fields that can be written in Hamilton-Jacobi-Bellman and Isaacs form and those arising in the recent theory of Mean Field Games, where the prototype model is described by a coupled system of PDEs involving a backward Hamilton-Jacobi and a forward Fokker-Planck equation. The thesis is divided in three parts. The first part is devoted to analyze strong maximum principles for fully nonlinear second order degenerate PDEs structured on Hörmander vector fields, having as a particular example fully nonlinear subelliptic PDEs on Carnot groups. These results are achieved by introducing a notion of subunit vector field for these nonlinear degenerate operators in the spirit of the seminal works on linear equations. As a byproduct, we then prove some new strong comparison principles for equations that can be written in Hamilton-Jacobi-Bellman form and Liouville theorems for some second order fully nonlinear degenerate PDEs. The second part of the thesis deals with time-dependent fractional Mean Field Game systems. These equations arise when the dynamics of the average player is described by a stable Lévy process to which corresponds a fractional Laplacian as diffusion operator. More precisely, we establish existence and uniqueness of solutions to such systems of PDEs with regularizing coupling among the equations for every order of the fractional Laplacian $sin(0,1)$. The existence of solutions is addressed via the vanishing viscosity method and we prove that in the subcritical regime the equations are satisfied in classical sense, while if $sleq1/2$ we find weak energy solutions. To this aim, we develop an appropriate functional setting based on parabolic Bessel potential spaces. We finally show uniqueness of solutions both under the Lasry-Lions monotonicity condition and for short time horizons. The last part focuses on the regularizing effect of evolutive Hamilton-Jacobi equations with Hamiltonian having superlinear growth in the gradient and unbounded right-hand side. In particular, the analysis is performed both for viscous Hamilton-Jacobi equations and its fractional counterpart in the subcritical regime via a duality method. The results are accomplished exploiting the regularity of solutions to Fokker-Planck-type PDEs with rough velocity fields in parabolic Sobolev and Bessel potential spaces respectively.
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Götmark, Elin, and Kaj Nyström. "Boundary behaviour of non-negative solutions to degenerate sub-elliptic equations." Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-164532.

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Let X = {X-1, ..., X-m} be a system of C-infinity vector fields in R-n satisfying Hormander's finite rank condition and let Omega be a non-tangentially accessible domain with respect to the Carnot-Caratheodory distance d induced by X. We study the boundary behavior of non-negative solutions to the equation Lu = Sigma(i, j -1) X-i*(a(ij)X(j)u) = Sigma X-i, j=1(i)*(x)(aij(x)X-j(x)u(x)) = 0 for some constant beta >= 1 and for some non-negative and real-valued function lambda = lambda(x). Concerning kappa we assume that lambda defines an A(2)-weight with respect to the metric introduced by the system of vector fields X =, {X-1,..., X-m}. Our main results include a proof of the doubling property of the associated elliptic measure and the Holder continuity up to the boundary of quotients of non-negative solutions which vanish continuously on a portion of the boundary. Our results generalize previous results of Fabes et al. (1982, 1983) [18-20] (m = n, {X-(1), ..., X-m} = {partial derivative(x1), ...., partial derivative x(n)}, A is an A(2)-weight) and Capogna and Garofalo (1998) [6] (X = {X-1,..., X-m} satisfies Hormander's finite rank condition and X(x) equivalent to lambda A for some constant lambda). One motivation for this study is the ambition to generalize, as far as possible, the results in Lewis and Nystrom (2007, 2010, 2008) [35-38], Lewis et al. (2008) [34] concerning the boundary behavior of non-negative solutions to (Euclidean) quasi-linear equations of p-Laplace type, to non-negative solutions, to certain sub-elliptic quasi-linear equations of p-Laplace type.
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Schneider, Mathias. "Finite element approximation of some degenerate/singular elliptic and parabolic equations." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265861.

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Abedin, Farhan. "Harnack Inequality for a class of Degenerate Elliptic Equations in Non-Divergence Form." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/523174.

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Mathematics
Ph.D.
We provide two proofs of an invariant Harnack inequality in small balls for a class of second order elliptic operators in non-divergence form, structured on Heisenberg vector fields. We assume that the coefficient matrix is uniformly positive definite, continuous, and symplectic. The first proof emulates a method of E. M. Landis, and is based on the so-called growth lemma, which establishes a quantitative decay of oscillation for subsolutions. The second proof consists in establishing a critical density property for non-negative supersolutions, and then invoking the axiomatic approach developed by Di Fazio, Gutiérrez and Lanconelli to obtain Harnack’s inequality.
Temple University--Theses
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Chen, Hua, and Ke Li. "The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2009/3024/.

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Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.
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Floridia, Giuseppe. "Approximate multiplicative controllability for degenerate parabolic problems and regularity properties of elliptic and parabolic systems." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1051.

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This thesis consists of two parts, both related to the theory of parabolic equations and systems. The first part is devoted to control theory which studies the possibility of influencing the evolution of a given system by an external action called control. Here we address approximate controllability problems via multiplicative controls, motivated by our interest in some differential models for the study of climatology. In the second part of the thesis we address regularity issues on the local differentiability and H\"older regularity for weak solutions of nonlinear systems in divergence form. In order to improve readability, the two parts have been organized as completely independent chapters, with two separate introductions and bibliographies. All the new results of this thesis have been presented at conferences and workshops, and most of them appeared or are to appear as research articles in international journals. Related directions for future research are also outlined in body of the work.
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MORALES, DANIA GONZALEZ. "TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36440@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
PROGRAMA DE EXCELENCIA ACADEMICA
Esta tese tem o intuito do estudo da existência, não existência e estimativas a priori de soluções não negativas de alguns tipos de problemas elípticos degenerados coercivos e não coercivos com um termo adicional dependendo do gradiente. Dentre outras coisas, obtemos condições integrais generalizadas tipo Keller-Osserman para a existência e não existência de soluções. Também mostramos que condições adicionais e diferentes são necessárias quando p é maior ou igual à 2 ou p é menor ou igual à 2, devido ao caráter degenerado do operador. As estimativas a priori são obtidas para super-soluções e soluções de EDPs elípticas superlineares o sistemas de tais tipos de equações em forma divergente com diferentes operadores e não linearidades. Além do mais, obtemos extensões até a fronteira de algumas desigualdades de Harnack fracas e lemas quantitativos de Hopf para operadores elípticos como o p-Laplaciano.
This thesis concerns the study of existence, nonexistence and a priori estimates of nonnegative solutions of some types of degenerate coercive and non coercive elliptic problems involving an additional term which depends on the gradient. Among other things, we obtain generalized integral conditions of Keller-Osserman type for the existence and nonexistence of solutions. Also, we show that different conditions are needed when p is higher or equal to 2 or p is less than or equal to 2, due to the degeneracy of the operator. The uniform a priori estimates are obtained for supersolutions and solutions of superlinear elliptic PDE or systems of such PDE in divergence form that can contain different operators and nonlinearities. We also give full boundary extensions to some half Harnack inequalities and quantitative Hopf lemmas, for degenerate elliptic operators like the p-Laplacian.
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Nguyen, Phuoc Tai. "Trace au bord de solutions d'équations de Hamilton-Jacobi elliptiques et trace initiale de solutions d'équations de la chaleur avec absorption sur-linéaire." Phd thesis, Université François Rabelais - Tours, 2012. http://tel.archives-ouvertes.fr/tel-00710410.

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Cette thèse est constituée de trois parties. Dans la première partie, on s'intéresse au problème de trace au bord d'une solution positive de l'équation de Hamilton-Jacobi (E1) $-\Delta u+g(|\nabla u|)=0$ dans un domaine borné $\Omega$ de ${\mathbb R}^N$, satisfaisant (E2) $u = \mu$ sur $\partial \Omega$. Si $g(r) \geq r^q$ avec $q > 1$, on prouve que toute solution positive de (E1) admet une trace au bord considérée comme une mesure de Borel régulière, pas nécessairement localement bornée. Si $g(r) = r^q$ avec $1 < q < q_c = \frac{N+1}{N}$ , on montre l'existence d'une solution positive dont la trace au bord est une mesure de Borel régulière $\nu \not \equiv \infty$ et on caractérise les singularités frontières isolées de solutions positives. Si $g(r) = r^q$ avec $q_c \leq q < 2$, on établit une condition nécessaire de résolution en terme de capacité de Bessel $C_{\frac{2-q}{q},q'} . On étudie aussi des ensembles éliminables au bord pour des solutions modérées. La deuxième partie est consacrée à étudier la limite, lorsque $k \to \infty$, de solutions d'équation $\partial_t u - \Delta u + f(u) =0$ dans ${\mathbb R}^N \times (0;\infty)$ avec donnée initiale $k\delta_0$ où $0$ est la masse de Dirac concentrée à l'origine et f est une fonction positive, continue, croissante et satisfaisant $f(0) = f^{-1}(0) = 0$. On prouve, sous certaines hypothèses portant sur f, qu'il existe essentiellement trois types de comportement possible en fonction des valeurs finies ou infinies des intégrales $\int_1^\infty f^{-1}(s)ds$ et $\int_1^\infty F^{-1/2}(s)ds$, où $F(s)=\int_0^s f(r)dr$. Grâce à ces résultats, on donne une nouvelle construction de la trace initiale et quelques résultats d'unicité et de non-unicité de solutions dont la donnée initiale n'est pas bornée. Dans la troisième partie, on élargit le cadre de nos investigations et généralise les résultats obtenus dans la deuxième partie au cas où l'opérateur est non-linéaire. En particulier, on s'intéresse à des propriétés qualitatives de solutions positives de l'équation $ \partial_t u-\Delta_p u+f(u)=0$ où $p > 1, \Delta_p u = div(\abs{\nabla u}^{p-2}\nabla u)$ et $f$ est une fonction continue, croissante, positive et satisfaisant $f(0) = 0 = f^{-1}(0)$. Si $p > \frac{2N}{N+1}$, on fournit une condition suffisante portant sur f pour l'existence et l'unicité des solutions fondamentales de données initiales $k\delta_0$ et on étudie la limite, lorsque $k \to \infty$, qui dépend du fait que $f^{-1}$ et $F^{-1/p}$ soient intégrables à l'infini ou pas, où $F(s) =\int_0^s f(r)dr. On donne aussi de nouveaux résultats de non-unicité de solutions avec donnée initiale non bornée. Si $p \geq 2$, on prouve que toute solution positive admet une trace initiale dans la classe de mesures de Borel régulières positives. Finalement on applique les résultats ci-dessus au cas modèle $f(u)=u^\alpha \ln^\beta(u+1)$ avec $\alpha>0$ et $\beta>0$.
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Mombourquette, Ethan. "On Holder continuity of weak solutions to degenerate linear elliptic partial differential equations." 2013. http://hdl.handle.net/10222/35442.

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For degenerate elliptic partial differential equations, it is often desirable to show that a weak solution is smooth. The first and most difficult step in this process is establishing local Hölder continuity. Sufficient conditions for establishing continuity have already been documented in [FP], [SW1], and [MRW], and their necessity in [R]. However, the complexity of the equations discussed in those works makes it difficult to understand the core structure of the arguments employed. Here, we present a harmonic-analytic method for establishing Hölder continuity of weak solutions in context of a simple linear equation div(Q?u) = f in a homogeneous space structure in order to showcase the form of the argument. Ad- ditionally, we correct an oversight in the adaptation of the John-Nirenberg inequality presented in [SW1], restricting it to a much smaller class of balls.
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Books on the topic "Degenerate elliptic equation"

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Levendorskii, Serge. Degenerate Elliptic Equations. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6.

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Levendorskiĭ, Serge. Degenerate elliptic equations. Dordrecht: Kluwer, 1993.

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Tero, Kilpeläinen, and Martio O, eds. Nonlinear potential theory of degenerate elliptic equations. Oxford: Clarendon Press, 1993.

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A, Dzhuraev. Degenerate and other problems. Harlow, Essex, England: Longman Scientific and Technical, 1992.

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On first and second order planar elliptic equations with degeneracies. Providence, R.I: American Mathematical Society, 2011.

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Colombo, Maria. Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations. Pisa: Scuola Normale Superiore, 2017. http://dx.doi.org/10.1007/978-88-7642-607-0.

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Popivanov, Peter R. The degenerate oblique derivative problem for elliptic and parabolic equations. Berlin: Akademie Verlag, 1997.

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Elliptic, hyperbolic and mixed complex equations with parabolic degeneracy. Singapore: World Scientific, 2008.

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Colombo, Maria. Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations: With Applications to the Vlasov-Poisson and Semigeostrophic Systems. Pisa: Scuola Normale Superiore, 2017.

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1943-, Gossez J. P., and Bonheure Denis, eds. Nonlinear elliptic partial differential equations: Workshop in celebration of Jean-Pierre Gossez's 65th birthday, September 2-4, 2009, Université libre de Bruxelles, Belgium. Providence, R.I: American Mathematical Society, 2011.

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Book chapters on the topic "Degenerate elliptic equation"

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Ji, Xinhua. "The Möbius Transformation, Green Function and the Degenerate Elliptic Equation." In Clifford Algebras and their Applications in Mathematical Physics, 17–35. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1374-1_2.

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Colombo, Maria. "The continuity equation with an integrable damping term." In Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations, 99–117. Pisa: Scuola Normale Superiore, 2017. http://dx.doi.org/10.1007/978-88-7642-607-0_5.

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Ciraolo, Giulio. "A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals." In Geometric Properties for Parabolic and Elliptic PDE's, 67–83. Milano: Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2841-8_5.

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Nirenberg, Louis. "Uniqueness in the Cauchy Problem for a Degenerate Elliptic Second Order Equation." In Differential Geometry and Complex Analysis, 213–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-69828-6_16.

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Kogut, Peter I., and Olha P. Kupenko. "Optimality Conditions for $$L^1$$ L 1 -Control in Coefficients of a Degenerate Nonlinear Elliptic Equation." In Advances in Dynamical Systems and Control, 429–71. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40673-2_24.

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Levendorskii, Serge. "Introduction." In Degenerate Elliptic Equations, 1–8. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6_1.

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Levendorskii, Serge. "General Schemes of Investigation of Spectral Asymptotics for Degenerate Elliptic Equations." In Degenerate Elliptic Equations, 279–300. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6_10.

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Levendorskii, Serge. "Spectral Asymptotics of Degenerate Elliptic Operators." In Degenerate Elliptic Equations, 301–34. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6_11.

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Levendorskii, Serge. "Spectral Asymptotics of Hypoelliptic Operators with Multiple Characteristics." In Degenerate Elliptic Equations, 335–87. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6_12.

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Levendorskii, Serge. "General Calculus of Pseudodifferential Operators." In Degenerate Elliptic Equations, 9–73. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6_2.

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Conference papers on the topic "Degenerate elliptic equation"

1

Bo, Hong, and Du Yaqin. "A Reverse HöLDER Inequality for the Gradient Estimates of Some Degenerate Elliptic Equation." In 2011 International Conference on Intelligent Computation Technology and Automation (ICICTA). IEEE, 2011. http://dx.doi.org/10.1109/icicta.2011.380.

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LAISTER, R., and R. E. BEARDMORE. "BIFURCATIONS IN DEGENERATE ELLIPTIC EQUATIONS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0090.

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Luyen, D. T., and N. M. Tri. "On boundary value problem for semilinear degenerate elliptic differential equations." In THE 5TH INTERNATIONAL CONFERENCE ON RESEARCH AND EDUCATION IN MATHEMATICS: ICREM5. AIP, 2012. http://dx.doi.org/10.1063/1.4724110.

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SALAKHITDINOV, M. S., and A. HASANOV. "THE FUNDAMENTAL SOLUTION FOR ONE CLASS OF DEGENERATE ELLIPTIC EQUATIONS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0048.

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Akdim, Youssef. "Solvability of quasilinear degenerated elliptic equations with L1 data." In Proceedings of the Conference in Mathematics and Mathematical Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814295574_0021.

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TIAN, FENG, and GUO-CHUN WEN. "THE RIEMANN-HILBERT PROBLEM FOR DEGENERATE ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER." In Proceedings of the Third International Conference. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814327862_0006.

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Ouaarabi, Mohamed El, Chakir Allalou, and Adil Abbassi. "On the Dirichlet Problem for some Nonlinear Degenerated Elliptic Equations with Weight." In 2021 7th International Conference on Optimization and Applications (ICOA). IEEE, 2021. http://dx.doi.org/10.1109/icoa51614.2021.9442620.

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