Bounds for the volume of the solutions to a system on the annulus

TL;DR

This paper establishes bounds on the volume of solutions to certain elliptic systems with weighted conditions and nonlinearities on an annulus, contributing to the understanding of solution behavior in these complex settings.

Contribution

It provides new bounds for the volume of solutions to elliptic systems with weighted nonlinearities and boundary singularities on an annulus, extending existing theoretical results.

Findings

Boundedness of the volume of solutions is proven.

Results apply to systems with exponential nonlinearities and boundary singularities.

The work advances understanding of elliptic systems with complex weights.

Abstract

We consider an elliptic system with regular H{\"o}lderian weight and exponential nonlinearity or with weight and boundary singularity, and, Dirichlet condition. We prove the boundedness of the volume of the solutions to those systems on the annulus.