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arXiv · 2203.03891

Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets

Renming Song·Peixue Wu·Shukun Wu
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Abstract

Let $D$ be an open set of $\mathbb{R}^d$, $α\in (0, 2)$ and let $\mathcal{L}_α^D$ be the generator of the censored $α$-stable process in $D$. In this paper, we establish sharp two-sided heat kernel estimates for $\mathcal{L}_α^D-κ$, with $κ$ being a non-negative critical potential and $D$ being a $C^{1, β}$ open set, $β\in ((α-1)_+,1]$. The potential $κ$ can exhibit multi-singularities and our regularity assumption on $D$ is weaker than the regularity assumed in earlier literature on heat kernel estimates of fractional Laplacians.

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Renming Song, Peixue Wu, Shukun Wu. 2024-12-22. Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets. https://doi.org/10.1016/j.spa.2025.104727

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