Gradient and Transport Estimates for Heat Flow on Nonconvex Domains
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866915135865487360 |
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| author | Sturm, Karl-Theodor |
| author_facet | Sturm, Karl-Theodor |
| contents | For the Neumann heat flow on nonconvex Riemannian domains $D\subset M$, we provide sharp gradient estimates and transport estimates with a novel $\sqrt t$-dependence, for instance, $$\text{Lip}( P^D_tf)\le e^{2S \, \sqrt{t/π}+\mathcal{O}(t)}\cdot \text{Lip} (f),$$ and we provide an equivalent characterization of the lower bound $S$ on the second fundamental form of the boundary in terms of these quantitative estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient and Transport Estimates for Heat Flow on Nonconvex Domains Sturm, Karl-Theodor Analysis of PDEs Differential Geometry Functional Analysis Probability For the Neumann heat flow on nonconvex Riemannian domains $D\subset M$, we provide sharp gradient estimates and transport estimates with a novel $\sqrt t$-dependence, for instance, $$\text{Lip}( P^D_tf)\le e^{2S \, \sqrt{t/π}+\mathcal{O}(t)}\cdot \text{Lip} (f),$$ and we provide an equivalent characterization of the lower bound $S$ on the second fundamental form of the boundary in terms of these quantitative estimates. |
| title | Gradient and Transport Estimates for Heat Flow on Nonconvex Domains |
| topic | Analysis of PDEs Differential Geometry Functional Analysis Probability |
| url | https://arxiv.org/abs/2502.01915 |