Regular solutions for nonlinear elliptic equations, with convective terms, in Orlicz spaces

TL;DR

This paper proves existence and regularity results for nonlinear elliptic equations with convection terms in Orlicz Sobolev spaces, using sub and supersolutions methods under general growth conditions.

Contribution

It introduces new existence and regularity results for quasilinear elliptic equations with convection terms in Orlicz spaces, expanding the theoretical framework.

Findings

Existence of solutions under general growth conditions

Regularity results for solutions in Orlicz Sobolev spaces

Application of sub and supersolutions method in this context

Abstract

We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in the Orlicz Sobolev spaces and under general growth conditions on the convection term. The sub and supersolutions method is a key tool in the proof of the existence results.