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.File in questo prodotto:
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