Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces
Published inAnnali di Matematica Pura ed Applicata
© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2013. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
We prove optimal integrability results for solutions of the p(·)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L 1 to variable exponent weak Lebesgue spaces.