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

Abstract

© 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. 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 L1. 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.