Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

Creators: Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe

Others:: SNS Pisa (SNS) ; SNS Isa; Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA); Dipartimento di matematica F. Casorati ; Università degli Studi di Pavia = University of Pavia (UNIPV)

Description

We compare several notion of weak (modulus of) gradient in metric measure spaces. Using tools from optimal transportation theory we prove density in energy of Lipschitz maps independenly of doubling and Poincaré assumptions on the metric measure space.

Abstract

(v3) A simpler axiomatization of weak gradients, still equivalent to all other ones, has been proposed (Lemma 2.1 and Remark 4.10). The density of Lipschitz functions has been slightly enforced (Sect. 8.3). Formula (4.7) and Proposition 5.4 (of v2) removed, more details added (end of page 18). Minor typos

Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

Description

Abstract

Additional details