Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

TL;DR

This paper establishes optimal integrability results for solutions to variable exponent p-Laplace equations by analyzing how Riesz and Wolff potentials map functions between variable exponent weak Lebesgue spaces, advancing understanding of elliptic PDEs.

Contribution

It demonstrates that variable exponent Riesz and Wolff potentials map L^1 functions into variable exponent weak Lebesgue spaces, providing new tools for PDE regularity analysis.

Findings

Optimal integrability results for p(·)-Laplace solutions

Mapping properties of Riesz and Wolff potentials in variable exponents

Extension of potential theory to variable exponent weak Lebesgue spaces

Abstract

We prove optimal integrability results for solutions of the $p(\cdot)$-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials maps $L^1$ to variable exponent weak Lebesgue spaces.