Sobolev and BV functions on $\mathrm{RCD}$ spaces via the short-time behaviour of the heat kernel
| Autor: | Brena, Camillo, Pasqualetto, Enrico, Pinamonti, Andrea |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | In the setting of finite-dimensional $\mathrm{RCD}(K,N)$ spaces, we characterize the $p$-Sobolev spaces for $p\in(1,\infty)$ and the space of functions of bounded variation in terms of the short-time behaviour of the heat flow. Moreover, we prove that Cheeger $p$-energies and total variations can be computed as limits of nonlocal functionals involving the heat kernel. Comment: 28 pages |
| Databáze: | arXiv |
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