Nonlocal parabolic De Giorgi classes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911432949366784 |
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| author | Ciani, Simone Nakamura, Kenta |
| author_facet | Ciani, Simone Nakamura, Kenta |
| contents | We study the local behavior of the elements of a specific energy class of functions, called the nonlocal parabolic ($p$-homogenous) De Giorgi class. First we carry on an analysis of their local boundedness under optimal tail conditions, and then prove several weak Harnack inequalities, measure theoretical propagation lemmas, and a parabolic Harnack inequality. We show a full proof of the local Hölder continuity, eventually establishing a Liouville-type rigidity property. Finally, as an application of our method, we prove a state-of-the-art nonlocal Harnack inequality for nonnegative solutions of the nonlocal Trudinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal parabolic De Giorgi classes Ciani, Simone Nakamura, Kenta Analysis of PDEs 35B65, 35R09, 47G20 We study the local behavior of the elements of a specific energy class of functions, called the nonlocal parabolic ($p$-homogenous) De Giorgi class. First we carry on an analysis of their local boundedness under optimal tail conditions, and then prove several weak Harnack inequalities, measure theoretical propagation lemmas, and a parabolic Harnack inequality. We show a full proof of the local Hölder continuity, eventually establishing a Liouville-type rigidity property. Finally, as an application of our method, we prove a state-of-the-art nonlocal Harnack inequality for nonnegative solutions of the nonlocal Trudinger equation. |
| title | Nonlocal parabolic De Giorgi classes |
| topic | Analysis of PDEs 35B65, 35R09, 47G20 |
| url | https://arxiv.org/abs/2508.16247 |