About Brezis-Merle Problem with Lipschitz condition

TL;DR

This paper analyzes boundary blow-up behavior in the Brezis-Merle problem, establishing compactness results under Lipschitz conditions and weaker domain regularity assumptions.

Contribution

It provides new blow-up analysis and compactness proofs for the Brezis-Merle problem with Lipschitz boundary conditions and less regular domains.

Findings

Boundary blow-up analysis for Brezis-Merle problem

Compactness result under Lipschitz boundary condition

Weaker regularity assumptions on domain sufficiency

Abstract

We give blow-up analysis for a Brezis-Merle's problem on the boundary. Also we give a proof of a compactness result with Lipschitz condition and weaker assumption on the regularity of the domain (smooth domain or $ C^{2,\alpha} $ domain).