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arXiv · 2410.19243

Global Calder\'on-Zygmund theory for fractional Laplacian type equations

Sun-Sig Byun·Kyeong Bae Kim·Deepak Kumar
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Abstract

We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calder\'on-Zygmund type estimates of $u/d^s$ depending on the regularity assumptions on the associated kernel coefficient including VMO, Dini continuity or the H\"older continuity, where $u$ is a weak solution to such a nonlocal problem and $d$ is the distance to the boundary function of a given domain. Our analysis is based on point-wise behaviors of maximal functions of $u/d^s$.

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Sun-Sig Byun, Kyeong Bae Kim, Deepak Kumar. 2024-10-25. Global Calder\'on-Zygmund theory for fractional Laplacian type equations. https://arxiv.org/abs/2410.19243

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