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
Lisini, Stefano 1
@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},
year = {2016},
publisher = {EDP Sciences},
volume = {22},
number = {3},
doi = {10.1051/cocv/2015020},
zbl = {1348.49048},
mrnumber = {3527938},
language = {en},
url = {https://www.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 - https://www.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 https://www.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, Tome 22 (2016) no. 3, pp. 670-687. doi: 10.1051/cocv/2015020
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