Calculus of Variations and Geometric Measure Theory

L. Ambrosio - N. Gigli - G. Savaré

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

created by ambrosio on 14 Nov 2011
modified on 14 Nov 2012


Submitted Paper

Inserted: 14 nov 2011
Last Updated: 14 nov 2012

Year: 2011


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.

Tags: GeMeThNES
Keywords: Upper gradient, Generalized gradient, Metric Sobolev spaces