# A compactness result for a system with weight and boundary singularity

## TL;DR

This paper investigates the blow-up behavior and compactness properties of solutions to an elliptic system with boundary singularities and weighted conditions, providing new insights into the system's solution structure.

## Contribution

It presents a novel compactness result for elliptic systems with boundary singularities and weighted conditions, extending previous understanding of solution behavior.

## Key findings

- Established blow-up behavior for solutions with boundary singularities.
- Proved a compactness theorem for systems with Hölderian weights and boundary singularities.
- Demonstrated conditions under which solutions remain bounded or blow up.

## Abstract

We give blow-up behavior for solutions to an elliptic system with Dirichlet condition, and, weight and boundary singularity. Also, we have a compactness result for this elliptic system with regular H{\"o}lderian weight and boundary singularity and Lipschitz condition.