The Poisson problem in domains with Ahlfors regular boundary

TL;DR

This paper proves the well-posedness of the Poisson problem for elliptic equations in complex domains with Ahlfors regular boundaries, using weighted Lebesgue spaces for data.

Contribution

It extends the understanding of elliptic PDEs by establishing well-posedness in weak local John domains with broad data conditions.

Findings

Well-posedness established for Poisson problem in Ahlfors regular boundary domains.

Applicable to linear second order elliptic equations with real coefficients.

Uses weighted Lebesgue spaces with broad parameter ranges.

Abstract

We establish well posedness of the Poisson problem in weak local John domains, for linear second order elliptic equations with real coefficients, and with data in weighted Lebesgue spaces with a very broad range of acceptable parameters.