Hölder regularity for a class of doubly non linear PDEs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915571673595904 |
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| author | Cassanello, Filippo Maria Henriques, Eurica |
| author_facet | Cassanello, Filippo Maria Henriques, Eurica |
| contents | We prove local Hölder continuity for non negative, locally bounded, local weak solutions to the class of doubly nonlinear parabolic equations $\partial_t (u_q) - \text{div} (|Du|^{p-2} Du) = 0$ for $p > 2$, $ 0 < q < p-1$. The proof relies on expansion of positivity results combined with the study of an alternative (related to DeGiorgi-type lemmas) and an exponential shift which allows us to deal with the intrinsic geometry associated to the problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder regularity for a class of doubly non linear PDEs Cassanello, Filippo Maria Henriques, Eurica Analysis of PDEs 35K55, 35B65, 35K65, 35Q35 We prove local Hölder continuity for non negative, locally bounded, local weak solutions to the class of doubly nonlinear parabolic equations $\partial_t (u_q) - \text{div} (|Du|^{p-2} Du) = 0$ for $p > 2$, $ 0 < q < p-1$. The proof relies on expansion of positivity results combined with the study of an alternative (related to DeGiorgi-type lemmas) and an exponential shift which allows us to deal with the intrinsic geometry associated to the problem. |
| title | Hölder regularity for a class of doubly non linear PDEs |
| topic | Analysis of PDEs 35K55, 35B65, 35K65, 35Q35 |
| url | https://arxiv.org/abs/2510.20432 |