Dirichlet problem for a class of nonlinear degenerate elliptic operators with critical growth and logarithmic perturbation

TL;DR

This paper studies the existence of weak solutions for a class of nonlinear degenerate elliptic Dirichlet problems involving critical growth and logarithmic perturbations, expanding understanding of such complex PDEs.

Contribution

It introduces new existence results for degenerate elliptic problems with critical nonlinearity and logarithmic perturbations, addressing gaps in current PDE theory.

Findings

Existence of weak solutions established under certain conditions.

Extension of solution theory to problems with critical growth and logarithmic terms.

New analytical techniques developed for degenerate elliptic operators.

Abstract

In this paper, we investigate the existence of weak solutions for a class of degenerate elliptic Dirichlet problems with critical nonlinearity and a logarithmic perturbation