On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices in Unbounded Domains

Abstract

For a class of second-order anisotropic elliptic equations with variable nonlinearity indices and summable right-hand sides, we consider the Dirichlet problem in arbitrary unbounded domains. We prove the existence and uniqueness of entropy solutions in anisotropic Sobolev spaces with variable exponents.

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Correspondence to L. M. Kozhevnikova.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 3, Differential and Functional Differential Equations, 2017.

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Kozhevnikova, L.M. On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices in Unbounded Domains. J Math Sci (2021). https://doi.org/10.1007/s10958-021-05262-0

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