The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918107059060736 |
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| author | Liu, Guanhua |
| author_facet | Liu, Guanhua |
| contents | This paper provides the general theory on parabolic Harnack inequalities (PHI, for short) for regular Dirichlet forms without killing part. We prove PHI by pure analytic methods, using both Nash and Moser approaches, and yield some important properties contained in PHI. Combining our recent result on weak Harnack inequalities, we greatly enlarge the list of equivalent characterizations of PHI. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis Liu, Guanhua Analysis of PDEs 34K30 (primary), 31C25, 35K08, 47D07, 60J46 (secondary) This paper provides the general theory on parabolic Harnack inequalities (PHI, for short) for regular Dirichlet forms without killing part. We prove PHI by pure analytic methods, using both Nash and Moser approaches, and yield some important properties contained in PHI. Combining our recent result on weak Harnack inequalities, we greatly enlarge the list of equivalent characterizations of PHI. |
| title | The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis |
| topic | Analysis of PDEs 34K30 (primary), 31C25, 35K08, 47D07, 60J46 (secondary) |
| url | https://arxiv.org/abs/2507.21604 |