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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/2602.07647 |
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| _version_ | 1866912887816060928 |
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| author | Cassanello, Filippo M. Ciani, Simone Iannizzotto, Antonio |
| author_facet | Cassanello, Filippo M. Ciani, Simone Iannizzotto, Antonio |
| contents | We prove several integral Harnack-type inequalities for local weak solutions of parabolic equations with measurable and bounded coefficients, describing singular s-fractional p-Laplacian diffusion. Then we apply the aforementioned estimates to evaluate the decay rate of the local mass and supremum of the solutions as they approach a possible extinction time. Yet we show consistency of our general decay estimates by studying the extinction phenomenon for weak solutions of the Cauchy-Dirichlet problem, by means of an approximation procedure that carefully avoids the use of an integrable time derivative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07647 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integral Harnack estimates and the rate of extinction of singular fractional diffusion Cassanello, Filippo M. Ciani, Simone Iannizzotto, Antonio Analysis of PDEs 35K67, 35B65, 35K92, 35Q35 We prove several integral Harnack-type inequalities for local weak solutions of parabolic equations with measurable and bounded coefficients, describing singular s-fractional p-Laplacian diffusion. Then we apply the aforementioned estimates to evaluate the decay rate of the local mass and supremum of the solutions as they approach a possible extinction time. Yet we show consistency of our general decay estimates by studying the extinction phenomenon for weak solutions of the Cauchy-Dirichlet problem, by means of an approximation procedure that carefully avoids the use of an integrable time derivative. |
| title | Integral Harnack estimates and the rate of extinction of singular fractional diffusion |
| topic | Analysis of PDEs 35K67, 35B65, 35K92, 35Q35 |
| url | https://arxiv.org/abs/2602.07647 |