Entropy solutions of nonlinear elliptic equations with $L^1$-data and without strict monotonocity conditions in weighted Orlicz-Sobolev spaces

Abstract

In this paper, we study the existence of entropy solutions for a class of nonlinear elliptic problems in weighted Orlicz-Sobolev spaces of with the form Au + g(x, u) = f , where A(u) = −div (ρ(x)a(x, u, ∇u)) is a Leray-Lions operator defined from the weighted Orlicz-sobolev spaces W 1 0 L M (ρ, Ω) into its dual. The right hand side f ∈ L 1 (Ω), and the function a(x, s, ξ ) satisfies only the large monotonicity instead of the monotonicity strict.

On the some equations inequalities in Musielak-Orlicz spaces with measure data

“…In the setting of Musielak-Orlicz spaces and in the variational case, Benkirane and Sidi El vally [15] proved the existence of solutions for the obstacle elliptic problem where they generalized the work of Gossez and Mustonen in [19], there are several papers worth mentioning that deal with the existence solutions of elliptic and parabolic problems under various assumptions (see [13,25,24,21,12,22,23,11,14,3,4,2,5,7,6] for more details).…”