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.

DOI: 10.1051/cocv/2015020

Keywords: Spaces of probability measures, Wasserstein−Orlicz distance, absolutely continuous curves, superposition principle, geodesic in spaces of probability measures

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@article{COCV_2016__22_3_670_0, author = {Lisini, Stefano}, title = {Absolutely continuous curves in extended {Wasserstein\ensuremath{-}Orlicz} spaces}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {670--687}, publisher = {EDP-Sciences}, volume = {22}, number = {3}, year = {2016}, doi = {10.1051/cocv/2015020}, zbl = {1348.49048}, mrnumber = {3527938}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2015020/} }

TY - JOUR AU - Lisini, Stefano TI - Absolutely continuous curves in extended Wasserstein−Orlicz spaces JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 670 EP - 687 VL - 22 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015020/ DO - 10.1051/cocv/2015020 LA - en ID - COCV_2016__22_3_670_0 ER -

%0 Journal Article %A Lisini, Stefano %T Absolutely continuous curves in extended Wasserstein−Orlicz spaces %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 670-687 %V 22 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015020/ %R 10.1051/cocv/2015020 %G en %F COCV_2016__22_3_670_0

Lisini, Stefano. Absolutely continuous curves in extended Wasserstein−Orlicz spaces. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 3, pp. 670-687. doi : 10.1051/cocv/2015020. http://archive.numdam.org/articles/10.1051/cocv/2015020/

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