Calculus of Variations and Geometric Measure Theory

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
modified by rajala1 on 13 Jun 2019


Published Paper

Inserted: 4 may 2018
Last Updated: 13 jun 2019

Journal: SIAM Journal on Mathematical Analysis
Volume: 51
Number: 3
Pages: 2359–2371
Year: 2019
Doi: 10.1137/18M1186514

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.