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arXiv · 2207.02488

A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces

Panu Lahti·Andrea Pinamonti·Xiaodan Zhou
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Abstract

We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Compared with previous works, we consider more general functionals. We also give a counterexample in the case $p=1$ demonstrating that unlike in Euclidean spaces, in metric measure spaces the limit of the nonlocal functions is only comparable, not necessarily equal, to the variation measure $\| Df\|(\Omega)$.

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Panu Lahti, Andrea Pinamonti, Xiaodan Zhou. 2022-07-06. A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces. https://arxiv.org/abs/2207.02488

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