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

2017/12/18 by Ambrosio, Luigi, Bruè, Elia, Trevisan, Dario
#37C10 (Primary) #60H07 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1712.06315

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, ∞) spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings.

Related

• A note on Lusin-type approximation of Sobolev functions on Gaussian\n spaces
• Regularity of Lagrangian flows over RCD^*(K,N) spaces
• Global Lipschitz extension preserving local constants
• Sobolev algebras through heat kernel estimates
• Genericity of ergodicity for Sobolev homeomorphisms