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;
2013-01-01
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.File in questo prodotto:
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