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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 411, Pages 5–37 (Mi znsl5629)  
This article is cited in 8 scientific papers (total in 8 papers)

A continuous model of transportation revisited

L. Brascoa, M. Petracheb

a Laboratoire d'Analyse, Topologie, Probabilités, Aix-Marseille Université, 39 Rue Frédéric Joliot Curie, 13453 Marseille Cedex 13, France
b ETH, Departement Mathematik, Rämistrasse 101, 8092 Zürich, Switzerland
Full-text PDF (393 kB) Citations (8)
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Abstract: We review two models of optimal transport, where congestion effects during the transport can be possibly taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fields with given divergence. The second one is the model by Carlier et al. (SIAM J. Control Optim 47: 1330–1350, 2008), which in turn is the continuous reformulation of Wardrop's model on graphs. We discuss the extensions of these models to their natural functional analytic setting and show that they are indeed equivalent, by using Smirnov decomposition theorem for normal $1$-currents.
Key words and phrases: Monge–Kantorovich problem, Beckmann problem, Smirnov Theorem, flat norm.
Received: 25.02.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 196, Issue 2, Pages 119–137
DOI: https://doi.org/10.1007/s10958-013-1644-7
Bibliographic databases:
Document Type: Article
UDC: 517.972+517.958:531.32
Language: English
Citation: L. Brasco, M. Petrache, “A continuous model of transportation revisited”, Representation theory, dynamical systems, combinatorial methods. Part XXII, Zap. Nauchn. Sem. POMI, 411, POMI, St. Petersburg, 2013, 5–37; J. Math. Sci. (N. Y.), 196:2 (2014), 119–137
Citation in format AMSBIB
\Bibitem{BraPet13}
\by L.~Brasco, M.~Petrache
\paper A continuous model of transportation revisited
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXII
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 411
\pages 5--37
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5629}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3048266}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 196
\issue 2
\pages 119--137
\crossref{https://doi.org/10.1007/s10958-013-1644-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897075206}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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