Calculus of Variations and Geometric Measure Theory
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A. Gerolin - A. Kausamo - T. Rajala

Non-existence of optimal transport maps for the multi-marginal repulsive harmonic cost

created by gerolin on 04 May 2018



Inserted: 4 may 2018

Year: 2018

ArXiv: 1805.00417 PDF


We give an example of an absolutely continuous measure $\mu$ on $\mathbb R^d$, for any $d \ge 1$, such that no minimizer of the $3$-marginal harmonic repulsive cost with all marginals equal to $\mu$ is supported on a graph over the first variable.

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