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.
Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and RCD(K,∞) spaces
Ambrosio, Luigi
Membro del Collaboration Group
;BRUÈ, EliaMembro del Collaboration Group
;
2018
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.File in questo prodotto:
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