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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.20719 |
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| _version_ | 1866910672745398272 |
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| author | Cao, Shiping Chen, Zhen-Qing |
| author_facet | Cao, Shiping Chen, Zhen-Qing |
| contents | We obtain a uniform boundary Harnack principle (BHP) on any open sets for a large class of non-local operators on metric measure spaces under a jump measure comparability and tail estimate condition, and an upper bound condition on the distribution function for the exit times from balls. These conditions are satisfied by any non-local operator $\mathcal{L}$ that admits a two-sided mixed stable-like heat kernel bounds when the underlying metric measure spaces have volume doubling and reverse volume doubling properties. The results of this paper are new even for non-local operators on Euclidean spaces. In particular, our results give not only the scale invariant but also uniform BHP for the first time for non-local operators on Euclidean spaces of both divergence form and non-divergence form with measurable coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform boundary Harnack principle for non-local operators on metric measure spaces Cao, Shiping Chen, Zhen-Qing Probability We obtain a uniform boundary Harnack principle (BHP) on any open sets for a large class of non-local operators on metric measure spaces under a jump measure comparability and tail estimate condition, and an upper bound condition on the distribution function for the exit times from balls. These conditions are satisfied by any non-local operator $\mathcal{L}$ that admits a two-sided mixed stable-like heat kernel bounds when the underlying metric measure spaces have volume doubling and reverse volume doubling properties. The results of this paper are new even for non-local operators on Euclidean spaces. In particular, our results give not only the scale invariant but also uniform BHP for the first time for non-local operators on Euclidean spaces of both divergence form and non-divergence form with measurable coefficients. |
| title | Uniform boundary Harnack principle for non-local operators on metric measure spaces |
| topic | Probability |
| url | https://arxiv.org/abs/2410.20719 |