Existence and regularity results for nonlinear elliptic equations in Orlicz spaces

Abstract

We are concerned with the existence and regularity of the solutions to the Dirichlet problem, for a class of quasilinear elliptic equations driven by a general differential operator, depending on $$(x,u,\nabla u)$$ ( x , u , ∇ u ) , and with a convective term f. The assumptions on the members of the equation are formulated in terms of Young’s functions, therefore we work in the Orlicz-Sobolev spaces. After establishing some auxiliary properties, that seem new in our context, we present two existence and two regularity results. We conclude with several examples.