Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and $RCD(K,\infty)$ spaces
Functional Analysis
2018-09-24 v2 Metric Geometry
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 spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings.
Keywords
Cite
@article{arxiv.1712.06315,
title = {Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and $RCD(K,\infty)$ spaces},
author = {Luigi Ambrosio and Elia Bruè and Dario Trevisan},
journal= {arXiv preprint arXiv:1712.06315},
year = {2018}
}