ABSOLUTELY CONTINUOUS CURVES IN EXTENDED WASSERSTEIN-ORLICZ SPACES

作者：Lisini Stefano^*

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2016, 22(3): 670-687.

DOI：10.1051/cocv/2015020

• Spaces of probability measures
• Wasserstein-Orlicz distance
• absolutely continuous curves
• superposition principle
• geodesic in spaces of probability measures

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. Savare, Invent. Math. 195 (2014) 289-391.] An application to the geodesics of this Wasserstein-Orlicz space is also given.

• 出版日期2016-9