非严格凸运输费用的一个策略和||X-Y|| R2中的p
A strategy for non-strictly convex transport costs and the example of ||x-y||p in R2
摘要：
研究了一类具有凸但非严格凸费用的最最优输运问题的最优输运映射的存在性。我们给出了一个分解策略来解决这个问题。作为我们的策略的一部分，我们必须处理一些运输问题，独立的利益，与凸约束的位移。作为我们的策略的一个例子，我们证明了最优输运映射的存在性的情况下，源措施是绝对连续的关于勒贝格测度和运输成本的形式h（||X-Y||）且h严格凸增加，||. || \R 2中的任意范数。
英文摘要：
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.
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