The continuity equation on metric measure spaces
Gigli, Nicola; Han, Bang-Xian (2015), The continuity equation on metric measure spaces, Calculus of Variations and Partial Differential Equations, 53, 1. http://dx.doi.org/10.1007/s00526-014-0744-7
TypeArticle accepté pour publication ou publié
Journal nameCalculus of Variations and Partial Differential Equations
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Abstract (EN)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 .
Subjects / Keywordsmetric measure spaces
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