We compare several notions of weak (modulus of) gradients 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 Poincaré assumptions on the metric measure space.
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
SAVARE', GIUSEPPE
2013-01-01
Abstract
We compare several notions of weak (modulus of) gradients 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 Poincaré assumptions on the metric measure space.File in questo prodotto:
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