Dirichlet heat kernel estimates of subordinate diffusion processes with diffusive components in $C^{1, α}$ open sets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916228012965888 |
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| author | Wang, Jie-Ming |
| author_facet | Wang, Jie-Ming |
| contents | In this paper, we derive explicit sharp two-sided estimates of the Dirichlet heat kernels for a class of symmetric subordinate diffusion processes with diffusive components in $C^{1, α}(α\in (0, 1])$ open sets in $\mathbb R^d$ when the scaling order of the Laplace exponent of purely discontinuous part of the subordinator is between $0$ and $1$ including $1.$ The main result of this paper shows the stability of Dirichlet heat kernel estimates for such processes in $C^{1, α}$ open sets in the sense that the estimates depend on the divergence elliptic operator only via its uniform ellipticity constant and the Dini continuity modulus of the diffusion coefficients. As a corollary, we obtain the sharp two-sided estimates for Green functions of those processes in bounded $C^{1, α}$ open sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirichlet heat kernel estimates of subordinate diffusion processes with diffusive components in $C^{1, α}$ open sets Wang, Jie-Ming Probability In this paper, we derive explicit sharp two-sided estimates of the Dirichlet heat kernels for a class of symmetric subordinate diffusion processes with diffusive components in $C^{1, α}(α\in (0, 1])$ open sets in $\mathbb R^d$ when the scaling order of the Laplace exponent of purely discontinuous part of the subordinator is between $0$ and $1$ including $1.$ The main result of this paper shows the stability of Dirichlet heat kernel estimates for such processes in $C^{1, α}$ open sets in the sense that the estimates depend on the divergence elliptic operator only via its uniform ellipticity constant and the Dini continuity modulus of the diffusion coefficients. As a corollary, we obtain the sharp two-sided estimates for Green functions of those processes in bounded $C^{1, α}$ open sets. |
| title | Dirichlet heat kernel estimates of subordinate diffusion processes with diffusive components in $C^{1, α}$ open sets |
| topic | Probability |
| url | https://arxiv.org/abs/2403.06791 |