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

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

2011-11-16

arxiv.org/abs/1111.3730v2

Mathematics

Analysis of PDEs

(v2) More details added (end of page 19); the density of Lipschitz functions has been slightly enforced (Sect. 8.3); a simpler

Scientific paper

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.

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