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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.12065 |
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| _version_ | 1866915857622368256 |
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| author | Jesus, David Sobral, Aelson Urbano, José Miguel |
| author_facet | Jesus, David Sobral, Aelson Urbano, José Miguel |
| contents | We study the parabolic fractional $p-$Laplace equation $$\p_t u+(-Δ_p)^su = 0$$ in the degenerate range \(2 \leq p < 2/(1-s)\). We show that weak solutions are Lipschitz continuous in space and, if \(p > 1/(1-s)\), also in time. We also prove a comparison principle for both weak and viscosity solutions, and establish the equivalence between the two notions of solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12065 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractional $p$-caloric functions are Lipschitz Jesus, David Sobral, Aelson Urbano, José Miguel Analysis of PDEs 35B65, 35R11, 35B51, 35D40, 35K92 We study the parabolic fractional $p-$Laplace equation $$\p_t u+(-Δ_p)^su = 0$$ in the degenerate range \(2 \leq p < 2/(1-s)\). We show that weak solutions are Lipschitz continuous in space and, if \(p > 1/(1-s)\), also in time. We also prove a comparison principle for both weak and viscosity solutions, and establish the equivalence between the two notions of solution. |
| title | Fractional $p$-caloric functions are Lipschitz |
| topic | Analysis of PDEs 35B65, 35R11, 35B51, 35D40, 35K92 |
| url | https://arxiv.org/abs/2603.12065 |