Quasilinear elliptic problems with general growth and merely integrable, or measure, data

TL;DR

This paper investigates boundary value problems for quasilinear elliptic equations with Orlicz growth and integrable or measure data, establishing existence, uniqueness, and regularity of generalized solutions for both Dirichlet and Neumann cases.

Contribution

It extends the theory of quasilinear elliptic equations to include general growth conditions and measure data, providing new existence, uniqueness, and regularity results.

Findings

Existence and uniqueness of generalized solutions for L^1 and measure data.

Regularity results for solutions under Orlicz growth conditions.

Analysis of both Dirichlet and Neumann boundary problems.

Abstract

Boundary value problems for a class of quasilinear elliptic equations, with an Orlicz type growth and L^1 right-hand side are considered. Both Dirichlet and Neumann problems are contemplated. Existence and uniqueness of generalized solutions, as well as their regularity, are established. The case of measure right-hand sides is also analyzed.