On deterministic solutions for multi-marginal optimal transport with Coulomb cost

Bindini, Ugo; De Pascale, Luigi; Kausamo, Anna

doi:10.3934/cpaa.2022015

dc.contributor.author	Bindini, Ugo
dc.contributor.author	De Pascale, Luigi
dc.contributor.author	Kausamo, Anna
dc.date.accessioned	2022-02-07T13:20:44Z
dc.date.available	2022-02-07T13:20:44Z
dc.date.issued	2022
dc.identifier.citation	Bindini, U., De Pascale, L., & Kausamo, A. (2022). On deterministic solutions for multi-marginal optimal transport with Coulomb cost. <i>Communications on Pure and Applied Analysis</i>, <i>21</i>(4), 1189-1208. <a href="https://doi.org/10.3934/cpaa.2022015" target="_blank">https://doi.org/10.3934/cpaa.2022015</a>
dc.identifier.other	CONVID_104139744
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/79667
dc.description.abstract	In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane R2. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the partial positive result obtained by Colombo and Stra and give a necessary and sufficient condition for the radial Coulomb cost to coincide with a much simpler cost that corresponds to the situation where all three particles are aligned. Moreover, we produce an infinite class of regular counterexamples to the optimality of this family of maps.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	American Institute of Mathematical Sciences (AIMS)
dc.relation.ispartofseries	Communications on Pure and Applied Analysis
dc.rights	In Copyright
dc.subject.other	multimarginal optimal transportation
dc.subject.other	Monge-Kantorovich problem
dc.subject.other	duality theory
dc.subject.other	Coulomb cost
dc.subject.other	Density Functional Theory.
dc.title	On deterministic solutions for multi-marginal optimal transport with Coulomb cost
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-202202071421
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	1189-1208
dc.relation.issn	1534-0392
dc.relation.numberinseries	4
dc.relation.volume	21
dc.type.version	acceptedVersion
dc.rights.copyright	© 2021 American Institute of Mathematical Sciences
dc.rights.accesslevel	openAccess	fi
dc.subject.yso	matemaattinen optimointi
dc.subject.yso	tiheysfunktionaaliteoria
dc.subject.yso	variaatiolaskenta
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p17635
jyx.subject.uri	http://www.yso.fi/onto/yso/p28852
jyx.subject.uri	http://www.yso.fi/onto/yso/p11197
dc.rights.url	http://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi	10.3934/cpaa.2022015
jyx.fundinginformation	The second and third authors are partially supported by the project:Alcuni problemi di trasporto ottimo ed applicazioni of GNAMPA-INDAM, the second author is partially supported by Fondi di Ateneo of the University of Firenze, the third author was partially supported by the project Contemporary topics on multi-marginal optimal mass transportation, funded by the Finnish Postdoctoral Pool (Suomen Kulttuurisäätiö).
dc.type.okm	A1