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

Alexandre Almeida; Peter H\"ast\"o; Petteri Harjulehto; Teemu Lukkari

arxiv: 1211.1495 · v2 · pith:GZAVCP4Nnew · submitted 2012-11-07 · 🧮 math.FA · math.AP

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

Alexandre Almeida , Petteri Harjulehto , Peter H\"ast\"o , Teemu Lukkari This is my paper

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keywords exponentlebesguespacesvariableweakpotentialsrieszwolff

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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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