The Poisson and Stokes problems in nonconvex, Lipschitz polytopes

TL;DR

This paper establishes the well-posedness of Poisson and Stokes problems in weighted function spaces over nonconvex, Lipschitz polytopes, focusing on weights in the Muckenhoupt class with specific boundary regularity.

Contribution

It demonstrates well-posedness results for these PDEs in weighted spaces on nonconvex Lipschitz domains for a particular class of weights.

Findings

Well-posedness of Poisson and Stokes problems in weighted spaces.

Results apply to nonconvex, Lipschitz polytopes.

Focus on Muckenhoupt weights with no boundary singularities.

Abstract

We show the well-posedness of the Poisson and Stokes problems in weighted spaces over nonconvex, Lipschitz polytopes. For a particular range of $p$, we consider those weights in the Muckenhoupt class $A_p$ that have no singularities in a neighborhood of the boundary of the domain.