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The Monge-Ampère equation and its link to optimal transportation


Authors: Guido De Philippis and Alessio Figalli
Journal: Bull. Amer. Math. Soc. 51 (2014), 527-580
MSC (2010): Primary 35-02; Secondary 35J60, 35J96
DOI: https://doi.org/10.1090/S0273-0979-2014-01459-4
Published electronically: May 16, 2014
MathSciNet review: 3237759
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Abstract: We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampère type equations arising in that context.


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Additional Information

Guido De Philippis
Affiliation: Institut für Mathematik Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich (Switzerland)
Email: guido.dephilippis@math.uzh.ch

Alessio Figalli
Affiliation: The University of Texas at Austin, Mathematics Dept. RLM 8.100, 2515 Speedway Stop C1200, Austin, Texas 78712-1202
Email: figalli@math.utexas.edu

DOI: https://doi.org/10.1090/S0273-0979-2014-01459-4
Received by editor(s): September 25, 2013
Published electronically: May 16, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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