Calder\'on-Zygmund estimates for the fractional $p$-Laplacian

Lars Diening; Simon Nowak

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arXiv · 2303.02116

Calder\'on-Zygmund estimates for the fractional $p$-Laplacian

Lars Diening·Simon Nowak

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Abstract

We prove fine higher regularity results of Calder\'on-Zygmund-type for equations involving nonlocal operators modelled on the fractional $p$-Laplacian with possibly discontinuous coefficients of VMO-type. We accomplish this by establishing precise pointwise bounds in terms of certain fractional sharp maximal functions. This approach is new already in the linear setting and enables us to deduce sharp regularity results also in borderline cases.

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Lars Diening, Simon Nowak. 2023-03-03. Calder\'on-Zygmund estimates for the fractional $p$-Laplacian. https://arxiv.org/abs/2303.02116

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