An elliptic problem with two singularities

TL;DR

This paper investigates a Dirichlet problem involving a degenerate coercive elliptic operator with a singular right-hand side, demonstrating that the singularity can have a regularizing effect on solutions.

Contribution

It introduces a novel analysis of how singular right-hand sides influence solutions of degenerate elliptic equations, revealing regularizing effects.

Findings

Singular right-hand side can regularize solutions

Degenerate coercive operator studied in elliptic problems

Solutions exhibit improved regularity despite singular data

Abstract

We study a Dirichlet problem for an elliptic equation defined by a degenerate coercive operator and a singular right-hand side. We will show that the right-hand side has some regularizing effects on the solutions, even if it is singular.