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<p>We prove fine higher regularity results of Calderón-Zygmund-type for equations involving nonlocal operators modelled on the fractional <i>p</i>-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.</p>

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Calderón–Zygmund Estimates for the Fractional p-Laplacian

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  • 发表日期：

    2025年1月25日

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  • Lars Diening,
  • Simon Nowak

摘要

We prove fine higher regularity results of Calderón-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.