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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.09192 |
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| _version_ | 1866916657351360512 |
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| author | Kim, Panki Song, Renming Vondraček, Zoran |
| author_facet | Kim, Panki Song, Renming Vondraček, Zoran |
| contents | In this paper we study the potential theory of Dirichlet forms on the half-space $\mathbb{R}^d_+$ defined by the jump kernel $J(x,y)=|x-y|^{-d-α}\mathcal{B}(x,y)$ and the killing potential $κx_d^{-α}$, where $α\in (0, 2)$ and $\mathcal{B}(x,y)$ can blow up to infinity at the boundary. The jump kernel and the killing potential depend on several parameters. For all admissible values of the parameters involved and all $d \ge 1$, we prove that the boundary Harnack principle holds, and establish sharp two-sided estimates on the Green functions of these processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09192 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Potential theory of Dirichlet forms with jump kernels blowing up at the boundary Kim, Panki Song, Renming Vondraček, Zoran Probability Analysis of PDEs 60J45 In this paper we study the potential theory of Dirichlet forms on the half-space $\mathbb{R}^d_+$ defined by the jump kernel $J(x,y)=|x-y|^{-d-α}\mathcal{B}(x,y)$ and the killing potential $κx_d^{-α}$, where $α\in (0, 2)$ and $\mathcal{B}(x,y)$ can blow up to infinity at the boundary. The jump kernel and the killing potential depend on several parameters. For all admissible values of the parameters involved and all $d \ge 1$, we prove that the boundary Harnack principle holds, and establish sharp two-sided estimates on the Green functions of these processes. |
| title | Potential theory of Dirichlet forms with jump kernels blowing up at the boundary |
| topic | Probability Analysis of PDEs 60J45 |
| url | https://arxiv.org/abs/2208.09192 |