Geodesic
Absolutely continuous curves in extended Wasserstein−Orlicz spaces
Lisini, Stefano1
1 Dipartimento di Matematica “F.Casorati”, Università degli Studi di Pavia, 27100 Pavia, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 670-687

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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.

Reçu le :
DOI : 10.1051/cocv/2015020
Classification : 49J27, 49J52
Keywords: Spaces of probability measures, Wasserstein−Orlicz distance, absolutely continuous curves, superposition principle, geodesic in spaces of probability measures

Lisini, Stefano 1

1 Dipartimento di Matematica “F.Casorati”, Università degli Studi di Pavia, 27100 Pavia, Italy. 
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Lisini, Stefano. Absolutely continuous curves in extended Wasserstein−Orlicz spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 670-687. doi: 10.1051/cocv/2015020

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