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arXiv · 2008.05356

Higher integrability for nonlinear nonlocal equations with irregular kernel

Simon Nowak
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Abstract

We prove a higher regularity result for weak solutions to nonlinear nonlocal equations along the integrability scale of Bessel potential spaces $H^{s,p}$ under a mild continuity assumption on the kernel. By embedding, this also yields regularity in Sobolev-Slobodeckij spaces $W^{s,p}$. Our approach is based on a characterization of Bessel potential spaces in terms of a certain nonlocal gradient-type operator and a perturbation approach commonly used in the context of local elliptic equations in divergence form.

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Simon Nowak. 2020-08-11. Higher integrability for nonlinear nonlocal equations with irregular kernel. https://arxiv.org/abs/2008.05356

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