The Stokes and Poisson problem in variable exponent spaces

TL;DR

This paper extends classical PDE theories to variable exponent spaces, establishing existence results for Stokes and Poisson problems with inhomogeneous boundary conditions on bounded domains.

Contribution

It generalizes Calderon-Zygmund and Agmon-Douglis-Nirenberg theories to variable exponent spaces, proving existence of solutions for complex boundary value problems.

Findings

Existence of strong and weak solutions in variable exponent spaces

Generalization of classical PDE theories to variable exponent contexts

Applicability to bounded domains with C^{1,1} boundary

Abstract

We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove the existence of strong and weak solutions for bounded domains with C^{1,1} boundary with inhomogenous boundary values. The result is based on generalizations of the classical theories of Calderon-Zygmund and Agmon-Douglis-Nirenberg to variable exponent spaces.