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.
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 | Dimensione | Formato | |
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