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. © European Mathematical Society.

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

AMBROSIO, Luigi;
2013

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. © European Mathematical Society.
2013
Settore MAT/05 - Analisi Matematica
Optimal transport; Sobolev functions; Weak upper gradients;
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/30793
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