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arXiv · 2212.01950

Gradient regularity and first-order potential estimates for a class of nonlocal equations

Tuomo Kuusi·Simon Nowak·Yannick Sire
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Abstract

We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and H\"older spaces as well as pointwise bounds of the gradient in terms of Riesz potentials, leading to fine regularity results in many commonly used function spaces. The kernel of the integral operators involves a H\"older dependence in the variables and is not assumed to be translation invariant.

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Tuomo Kuusi, Simon Nowak, Yannick Sire. 2022-12-04. Gradient regularity and first-order potential estimates for a class of nonlocal equations. https://arxiv.org/abs/2212.01950

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