Calculus of Variations and Geometric Measure Theory

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
modified by bruè on 08 May 2019


Published Paper

Inserted: 8 jan 2018
Last Updated: 8 may 2019

Journal: Adv. Math.
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.