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arXiv · 2212.03910

Sobolev and BV functions on $\mathrm{RCD}$ spaces via the short-time behaviour of the heat kernel

Camillo Brena·Enrico Pasqualetto·Andrea Pinamonti
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Abstract

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.

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Camillo Brena, Enrico Pasqualetto, Andrea Pinamonti. 2022-12-07. Sobolev and BV functions on $\mathrm{RCD}$ spaces via the short-time behaviour of the heat kernel. https://arxiv.org/abs/2212.03910

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