Published Paper
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Inserted: 8 jan 2018
Last Updated: 11 nov 2026

Journal: Adv. Math.
Year: 2017

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.