Abstract:
The Dirichlet problem is considered in arbitrary domains for a class of second-order anisotropic elliptic equations with variable nonlinearity exponents and right-hand sides in L1L1. It is proved that an entropy solution exists in anisotropic Sobolev spaces with variable exponent. It is proved that the entropy solution obtained is a renormalized solution of the problem under consideration.
Bibliography: 37 titles.
Keywords:
anisotropic elliptic equation, entropy solution, renormalized solution, existence of a solution, variable exponent, Dirichlet problem.
Citation:
L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Sb. Math., 210:3 (2019), 417–446
\Bibitem{Koz19}
\by L.~M.~Kozhevnikova
\paper Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents
\jour Sb. Math.
\yr 2019
\vol 210
\issue 3
\pages 417--446
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Linking options:
https://www.mathnet.ru/eng/sm9078
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This publication is cited in the following 15 articles:
L. M. Kozhevnikova, “Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain”, Theoret. and Math. Phys., 218:1 (2024), 106–128
L. M. Kozhevnikova, “Suschestvovanie renormalizovannogo resheniya nelineinogo ellipticheskogo uravneniya s L1L1-dannymi v prostranstve Rn”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 2, Rossiiskii universitet druzhby narodov, M., 2024, 278–299
L. M. Kozhevnikova, “Entropy and Renormalized Solutions for a Nonlinear Elliptic Problem in Musielak–Orlicz Spaces”, J Math Sci, 2024
L. M. Kozhevnikova, “Existence of a Renormalized Solution of a Quasilinear Elliptic
Equation without the Sign Condition
on the Lower-Order Term”, Diff Equat, 60:6 (2024), 729
L. M Kozhevnikova, “EXISTENCE OF A RENORMALIZED SOLUTION OF A QUASI-LINEAR ELLIPTIC EQUATION WITHOUT THE SIGN CONDITION ON THE LOWEST TERM”, Differencialʹnye uravneniâ, 60:6 (2024), 764
L. M. Kozhevnikova, “Existence of a Renormalized Solution to a Nonlinear Elliptic Equation with L1-Data in the Space ℝn”, J Math Sci, 2024
L. M. Kozhevnikova, “Entropiinye i renormalizovannye resheniya nelineinoi ellipticheskoi zadachi v prostranstvakh Muzilaka—Orlicha”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 98–115
L. M. Kozhevnikova, “On solutions of nonlinear elliptic equations with L1-data in unbounded domains”, Lobachevskii J. Math., 44:5 (2023), 1879
A. P. Kashnikova, L. M. Kozhevnikova, “Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces”, Sb. Math., 213:4 (2022), 476–511
N. Dechoucha, F. Mokhtari, H. Ayadi, “Anisotropic degenerate elliptic problems in RN with variable exponent and locally integrable data”, J. Elliptic Parabol. Equ., 8:2 (2022), 939–957
L. M. Kozhevnikova, “Equivalence of entropy and renormalized solutions of the anisotropic elliptic problem in unbounded domains with measure data”, Russian Math. (Iz. VUZ), 64:1 (2020), 25–39
A. K. Gushchin, “Extensions of the space of continuous functions and embedding theorems”, Sb. Math., 211:11 (2020), 1551–1567
L. M. Kozhevnikova, “Renormalized solutions of elliptic equations with variable exponents and general measure data”, Sb. Math., 211:12 (2020), 1737–1776
Abdellaoui M., “Generalized Solutions For a Class of Nonlinear Parabolic Problems With Irregular Data in Unbounded Domains”, Adv. Oper. Theory, 5:4 (2020), 1839–1888
A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
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