The continuity equation on metric measure spaces View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-05

AUTHORS

Nicola Gigli, Bang-Xian Han

ABSTRACT

The aim of this paper is to show that it makes sense to write the continuity equation on a metric measure space (X,d,m) and that absolutely continuous curves (μt) w.r.t. the distance W2 can be completely characterized as solutions of the continuity equation itself, provided we impose the condition μt≤Cm for every t and some C>0. More... »

PAGES

149-177

References to SciGraph publications

  • 2014-02. Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below in INVENTIONES MATHEMATICAE
  • 2000-01. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem in NUMERISCHE MATHEMATIK
  • 2013. A User’s Guide to Optimal Transport in MODELLING AND OPTIMISATION OF FLOWS ON NETWORKS
  • 2007. Measure Theory in NONE
  • 2009. Optimal Transport, Old and New in NONE
  • 2007-01. Characterization of absolutely continuous curves in Wasserstein spaces in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00526-014-0744-7

    DOI

    http://dx.doi.org/10.1007/s00526-014-0744-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1050068909


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