A compactness result for solutions to an equation with boundary singularity

TL;DR

This paper investigates the blow-up behavior of solutions to a boundary singularity problem and establishes compactness results under Lipschitz conditions, contributing to the understanding of solution behavior near singularities.

Contribution

It provides a new analysis of blow-up behavior and proves compactness of solutions for equations with boundary singularities under Lipschitz conditions.

Findings

Characterization of blow-up behavior near boundary singularities

Proof of compactness of solutions under Lipschitz conditions

Insights into solution regularity near singular boundary points

Abstract

We give a blow-up behavior for solutions to a problem with singularity and with Dirichlet condition. An application, we have a compactness of the solutions to this Problem with singularity and Lipschitz conditions.