Summability of solutions of the Dirichlet problem for nonlinear elliptic equations with right-hand side in logarithmic classes close to [formula omitted

Abstract

In this paper, we consider the Dirichlet problem for a class of nonlinear elliptic second-order equations with right-hand side in L1. We describe the summability properties of entropy and weak solutions of this problem in the case where the right-hand side belongs to classes close to L1 and defined by the logarithmic function or its compositions of arbitrary multiplicity.