Global geometric estimates for the heat equation via duality methods
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916408514838528 |
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| author | Goffi, Alessandro Tralli, Giulio |
| author_facet | Goffi, Alessandro Tralli, Giulio |
| contents | We discuss first-order and second-order regularization effects for solutions to the classical heat equation. In particular we propose a global approach to study smoothing effects of Hamilton-Li-Yau type: such approach is nonlinear in spirit and it is based on the Bernstein method and duality techniques à la Evans. In a similar way, we also deal with the conservation of geometric properties for the heat flow as initiated by Brascamp-Lieb. In contrast to maximum principle methods based on sup-norm procedures, the integral method we adopt relies on contractivity properties for advection-diffusion equations and it applies to problems with homogeneous Neumann conditions posed equally on bounded and unbounded convex domains under suitable assumptions on their geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global geometric estimates for the heat equation via duality methods Goffi, Alessandro Tralli, Giulio Analysis of PDEs We discuss first-order and second-order regularization effects for solutions to the classical heat equation. In particular we propose a global approach to study smoothing effects of Hamilton-Li-Yau type: such approach is nonlinear in spirit and it is based on the Bernstein method and duality techniques à la Evans. In a similar way, we also deal with the conservation of geometric properties for the heat flow as initiated by Brascamp-Lieb. In contrast to maximum principle methods based on sup-norm procedures, the integral method we adopt relies on contractivity properties for advection-diffusion equations and it applies to problems with homogeneous Neumann conditions posed equally on bounded and unbounded convex domains under suitable assumptions on their geometry. |
| title | Global geometric estimates for the heat equation via duality methods |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.15456 |