Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents

L. M. Kozhevnikova

Sbornik. Mathematics, Tome 210 (2019) no. 3, pp. 417-446

Résumé

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 $L_1$. 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.

Détail

Keywords: entropy solution, renormalized solution, variable exponent, Dirichlet problem.
Mots-clés : anisotropic elliptic equation, existence of a solution

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