Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - E. Bruè - D. Trevisan

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

created by trevisan on 08 Jan 2018



Inserted: 8 jan 2018

Year: 2017

ArXiv: 1712.06315 PDF


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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