A strategy for non-strictly convex transport costs and the example of ||x-y||p in R2 Export

@article{citeulike:5790610, abstract = {This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat some transport problems, of independent interest, with a convex constraint on the displacement. As an illustration of our strategy, we prove existence of optimal transport maps in the case where the source measure is absolutely continuous with respect to the Lebesgue measure and the transportation cost is of the form h(||x-y||) with h strictly convex increasing and ||. || an arbitrary norm in \R2.}, archivePrefix = {arXiv}, author = {Carlier, Guillaume and De Pascale, Luigi and Santambrogio, Filippo}, citeulike-article-id = {5790610}, citeulike-linkout-0 = {http://arxiv.org/abs/0909.2804}, citeulike-linkout-1 = {http://arxiv.org/pdf/0909.2804}, day = {15}, eprint = {0909.2804}, keywords = {convex, d2, transport}, month = {Sep}, posted-at = {2009-09-16 07:45:45}, priority = {2}, title = {A strategy for non-strictly convex transport costs and the example of ||x-y||p in R2}, url = {http://arxiv.org/abs/0909.2804}, year = {2009} }

TY - JOUR ID - citeulike:5790610 L3 - citeulike-article-id:5790610 N2 - This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat some transport problems, of independent interest, with a convex constraint on the displacement. As an illustration of our strategy, we prove existence of optimal transport maps in the case where the source measure is absolutely continuous with respect to the Lebesgue measure and the transportation cost is of the form h(||x-y||) with h strictly convex increasing and ||. || an arbitrary norm in \R2. TI - A strategy for non-strictly convex transport costs and the example of ||x-y||p in R2 KW - convex KW - d2 KW - transport AU - Carlier, Guillaume AU - De Pascale, Luigi AU - Santambrogio, Filippo PY - 2009/Sep/15/ UR - http://arxiv.org/abs/0909.2804 ER -