Absolutely continuous curves in extended Wasserstein−Orlicz spaces
Dipartimento di Matematica “F.Casorati”, Università degli Studi di Pavia,
27100 Pavia, Italy.
In this paper we extend a previous result of the author [S. Lisini, Calc. Var. Partial Differ. Eq. 28 (2007) 85–120.] on the characterization of absolutely continuous curves in Wasserstein spaces to a more general class of spaces: the spaces of probability measures endowed with the Wasserstein−Orlicz distance constructed on extended Polish spaces (in general non separable), recently considered in [L. Ambrosio, N. Gigli and G. Savaré, Invent. Math. 195 (2014) 289–391.] An application to the geodesics of this Wasserstein−Orlicz space is also given.
Mathematics Subject Classification: 49J27 / 49J52
Key words: Spaces of probability measures / Wasserstein−Orlicz distance / absolutely continuous curves / superposition principle / geodesic in spaces of probability measures
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