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arXiv · 1712.06315

Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and $RCD(K,\infty)$ spaces

Luigi Ambrosio·Elia Bruè·Dario Trevisan
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Abstract

We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and $RCD(K, \infty)$ spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings.

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Luigi Ambrosio, Elia Bruè, Dario Trevisan. 2017-12-18. Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and $RCD(K,\infty)$ spaces. https://arxiv.org/abs/1712.06315

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