Uniform bound for the volume of the solutions of elliptic equations

TL;DR

This paper establishes a uniform bound on the volume of solutions to elliptic equations with specific boundary conditions and weights, contributing to the understanding of solution behavior in analytic domains.

Contribution

It provides a new uniform volume bound for solutions of elliptic equations with Hölderian weights or boundary singularities on analytic domains.

Findings

Bounded the volume of solutions under given conditions

Applicable to elliptic equations with boundary singularities

Enhances understanding of solution regularity in analytic domains

Abstract

We consider variational problems with regular H{\"o}lderian weight or boundary singularity, and Dirichlet condition. We prove the boundedness of the volume of the solutions to these equations on analytic domains.