Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data (Q2806544)
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scientific article; zbMATH DE number 6581959
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data |
scientific article; zbMATH DE number 6581959 |
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Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data (English)
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18 May 2016
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Density Functional Theory
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Monge-Kantorovich problem
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optimal transport problem
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spherically symmetric data
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The purpose of this paper is to show some counterexamples to the conjecture that there are cases in which there are no maps which are optimal in a certain Monge problem. This Monge problem consists in the minimization of the integral of the Coulomb interaction for a given probability measure. First many counterexamples and lemmas together with pictures are given. Finally, long proofs for non-quantitative lemmas are given.
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