Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets
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| Format: | Preprint |
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2022
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| _version_ | 1866915364437229568 |
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| author | Song, Renming Wu, Peixue Wu, Shukun |
| author_facet | Song, Renming Wu, Peixue Wu, Shukun |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_03891 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets Song, Renming Wu, Peixue Wu, Shukun Probability Analysis of PDEs 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. |
| title | Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2203.03891 |