Open AccessOn Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices
Author(s) -
Л. М. Кожевникова,
Л. М. Кожевникова
Publication year - 2017
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2017-63-3-475-493
Subject(s) - uniqueness , mathematics , sobolev space , nonlinear system , mathematical analysis , variable (mathematics) , anisotropy , entropy (arrow of time) , dirichlet distribution , dirichlet problem , pure mathematics , boundary value problem , physics , quantum mechanics
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.