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

Ambrosio Luigi - Gigli Nicola - Savaré Giuseppe

year: 2011
abstract: 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 Poincar\'e assumptions on the metric measure space.

The paper is available on the cvgmt preprint server.