On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces

Abstract

© 2017, Pleiades Publishing, Ltd.For a certain class of anisotropic elliptic equations with the right-hand side from L1 in an arbitrary unbounded domains, the Dirichlet problem with an inhomogeneous boundary condition is considered. The existence and uniqueness of the entropy solution in anisotropic Sobolev–Orlicz spaces are proven.