A compactness result for a Gelfand-Liouville system with Lipschitz condition

TL;DR

This paper provides a quantization analysis for a Gelfand-Liouville elliptic system with Dirichlet conditions and establishes a compactness result for systems satisfying a Lipschitz condition, advancing understanding of solution behavior.

Contribution

It introduces a quantization analysis for the Gelfand-Liouville system and proves a new compactness result under Lipschitz conditions, which was not previously known.

Findings

Quantization analysis of the elliptic system.

A new compactness theorem for Lipschitz conditions.

Enhanced understanding of solution behavior under Dirichlet conditions.

Abstract

We give a quantization analysis to an elliptic system (Gelfand-Liouville type system) with Dirichlet condition. An application, we have a com-pactness result for an elliptic system with Lipschitz condition.