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

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

Gigli, Nicola;
2013

Abstract

We compare several notion of weak (modulus of) gradient in metric measure spaces and prove their equivalence. Using tools from optimal transportation theory we prove density in energy of Lipschitz maps independently of doubling and Poincar ́e assumptions on the metric measure space.
29
3
969
996
https://arxiv.org/abs/1111.3730
Ambrosio, L.; Gigli, Nicola; Savaré, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/16654
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