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

BRUE', ELIA;Trevisan, Dario
2018-01-01

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.
2018
Ambrosio, Luigi; Brue', Elia; Trevisan, Dario
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/944993
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