By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case.
Keywords: optimal mass transportation theory, Monge − Kantorovich problem, calculus of variations, shape analysis, geometric measure theory
@article{COCV_2013__19_3_888_0, author = {Granieri, Luca and Maddalena, Francesco}, title = {Transport problems and disintegration maps}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {888--905}, publisher = {EDP-Sciences}, volume = {19}, number = {3}, year = {2013}, doi = {10.1051/cocv/2012037}, mrnumber = {3092366}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2012037/} }
TY - JOUR AU - Granieri, Luca AU - Maddalena, Francesco TI - Transport problems and disintegration maps JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 888 EP - 905 VL - 19 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2012037/ DO - 10.1051/cocv/2012037 LA - en ID - COCV_2013__19_3_888_0 ER -
%0 Journal Article %A Granieri, Luca %A Maddalena, Francesco %T Transport problems and disintegration maps %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 888-905 %V 19 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2012037/ %R 10.1051/cocv/2012037 %G en %F COCV_2013__19_3_888_0
Granieri, Luca; Maddalena, Francesco. Transport problems and disintegration maps. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 3, pp. 888-905. doi : 10.1051/cocv/2012037. http://archive.numdam.org/articles/10.1051/cocv/2012037/
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