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

Lars Diening; Simon Nowak

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

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arxiv 2303.02116 v1 pith:ZPULCUVO submitted 2023-03-03 math.AP

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

Lars Diening , Simon Nowak This is my paper

classification math.AP

keywords fractionalcalderlaplacianregularityresultssharpaccomplishalready

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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.

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

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