Abstract:
For a certain class of second-order anisotropic elliptic equations with variable nonlinearity indices and L1 right-hand side we consider the Dirichlet problem in arbitrary unbounded domains. We prove the existence and uniqueness of entropy solutions in anisotropic Sobolev spaces with variable indices.
Document Type:
Article
UDC:517.956.25
Language: Russian
Citation:
L. M. Kozhevnikova, “On entropy solutions of anisotropic elliptic equations with variable nonlinearity indices”, Differential and functional differential equations, CMFD, 63, no. 3, Peoples' Friendship University of Russia, M., 2017, 475–493
\Bibitem{Koz17}
\by L.~M.~Kozhevnikova
\paper On entropy solutions of anisotropic elliptic equations with variable nonlinearity indices
\inbook Differential and functional differential equations
\serial CMFD
\yr 2017
\vol 63
\issue 3
\pages 475--493
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd330}
\crossref{https://doi.org/10.22363/2413-3639-2017-63-3-475-493}
Linking options:
https://www.mathnet.ru/eng/cmfd330
https://www.mathnet.ru/eng/cmfd/v63/i3/p475
This publication is cited in the following 5 articles:
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
L. M. Kozhevnikova, “On solutions of anisotropic elliptic equations with variable exponent and measure data”, Complex Var. Elliptic Equ., 65:3 (2020), 333–367
L. M. Kozhevnikova, “Renormalized solutions of elliptic equations with variable exponents and general measure data”, Sb. Math., 211:12 (2020), 1737–1776
L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Sb. Math., 210:3 (2019), 417–446
N. A. Vorobev, F. Kh. Mukminov, “Suschestvovanie renormalizovannogo resheniya parabolicheskoi zadachi v anizotropnykh prostranstvakh Soboleva—Orlicha”, Differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 39–64
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