On the regularity and existence of weak solutions for a class of degenerate singular elliptic problem

TL;DR

This paper investigates the regularity and existence of weak solutions for a class of degenerate singular elliptic problems involving p-admissible weights that may vanish or blow up, with variable singularity inside the domain.

Contribution

It establishes new regularity and existence results for degenerate singular elliptic equations with variable singularity and weight functions.

Findings

Provided sufficient conditions for regularity of solutions

Proved existence of weak solutions under specified conditions

Extended understanding of degenerate singular elliptic problems

Abstract

In this article, we consider a class of degenerate singular problems. The degeneracy is captured by the presence of a class of $p$-admissible weights, which may vanish or blow up near the origin. Further, the singularity is allowed to vary inside the domain. We provide sufficient conditions on the weight function, on the singular exponent and the source function to establish regularity and existence results.