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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/779635
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