Solutions to multi-marginal optimal transport problems concentrated on several graphs
Abbas Moameni; Brendan Pass · 2015 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
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Abstract (excerpt)
We study solutions to the multi-marginal Monge-Kantorovich problem which are concentrated on several graphs over the first marginal. We first present two general conditions on the cost function which ensure, respectively, that any solution must concentrate on either finitely many or countably many graphs. We show that local differential conditions on the cost, known to imply local $d$-rectifiability of the solution, are sufficient to imply a local version of the first of our conditions. We exhibit two examples of cost functions satisfying our conditions, including the Coulomb cost from density
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Metadata source: arXiv