JournalsrmiVol. 29, No. 3pp. 969–996

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

  • Luigi Ambrosio

    Scuola Normale Superiore, Pisa, Italy
  • Nicola Gigli

    SISSA, Trieste, Italy
  • Giuseppe Savaré

    Università di Pavia, Italy
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces cover
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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.

Cite this article

Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré, Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 969–996

DOI 10.4171/RMI/746