Riesz and Wolff potentials and elliptic equations in 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.