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Essentially self-contained account of the known regularity theory of optimal maps in the case of quadratic cost
Presents proofs of some recent results like Sobolev regularity and Sobolev stability for optimal maps and their applications too the semi-geostrophic system
Proves for the first time a partial regularity theorem for optimal map with respect to a general cost function
Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 17)
Part of the book sub series: Theses (Scuola Normale Superiore) (TSNS)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
Authors and Affiliations
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Hausdorff Center for Mathematics, Bonn, Germany
Guido Philippis
Bibliographic Information
Book Title: Regularity of Optimal Transport Maps and Applications
Authors: Guido Philippis
Series Title: Publications of the Scuola Normale Superiore
DOI: https://doi.org/10.1007/978-88-7642-458-8
Publisher: Edizioni della Normale Pisa
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Scuola Normale Superiore 2013
Softcover ISBN: 978-88-7642-456-4Published: 05 September 2013
eBook ISBN: 978-88-7642-458-8Published: 28 June 2013
Series ISSN: 2239-1460
Series E-ISSN: 2532-1668
Edition Number: 1
Topics: Calculus of Variations and Optimal Control; Optimization