A sharp inequality for transport maps in W^{1,p}(R) via approximation

Details A sharp inequality for transport maps in W^{1,p}(R) via approximation A sharp inequality for transport maps in W^{1,p}(R) via approximation

2011-09-30

arxiv.org/abs/1109.6783v1

Mathematics

Analysis of PDEs

Scientific paper

For $f$ convex and increasing, we prove the inequality $ \int f(|U'|) \geq \int f(nT')$, every time that $U$ is a Sobolev function of one variable and $T$ is the non-decreasing map defined on the same interval with the same image measure as $U$, and the function $n(x)$ takes into account the number of pre-images of $U$ at each point. This may be applied to some variational problems in a mass-transport framework or under volume constraints.

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