Overview
- 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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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: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 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