Nonexistence of optimal transport maps for the multimarginal repulsive harmonic cost

Augusto Gerolin, Anna Kausamo, Tapio Rajala

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We give an example of an absolutely continuous measure μ on Rd for any d ≥ 1 such that no minimizer of the 3-marginal harmonic repulsive cost with all marginals equal to μ is supported on a graph over the first variable.

Original languageEnglish
Pages (from-to)2359-2371
Number of pages13
JournalSIAM Journal on Mathematical Analysis
Volume51
Issue number3
DOIs
Publication statusPublished - 1 Jan 2019
Externally publishedYes

Keywords

  • Monge problem
  • Multimarginal optimal transport
  • Optimal transport

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