On solutions of anisotropic elliptic equations with variable exponent and measure data

Abstract

© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group. The Dirichlet problem in arbitrary domains for a wide class of anisotropic elliptic equations of the second order with variable exponent nonlinearities and the right-hand side as a measure is considered. The existence of an entropy solution in anisotropic Sobolev spaces with variable exponents is established. It is proved that the obtained entropy solution is a renormalized solution of the considered problem.