Solvability of nonlinear multivalued elliptic problems involving degenerate coercivity with variable exponents and $L^{1}-$data.

Abstract

This paper is interested in studying existence results for a general class of nonlinear elliptic problems with variable exponents associated with the differential inclusion and degenerate coercivity.  We prove an existence of entropy solutions for this non-coercive differential inclusion. Moreover, we will give some regularity results for these solutions.