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

preprint2013arXivOpen access

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.

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

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