Abstract
The aim of this Chapter is to introduce the main ideas behind the regularity theory of Aleksandrov solutions to the Monge-Ampère equation and to give a proof of Caffarelli C 1,α regularity theorem [18, 20]. Many of the tools developed in this Chapter will play a crucial role in the proof of the Sobolev regularity in Chapter 3. In the last Section we show, without proofs, how to build smooth solutions to the Monge-Ampère equation throughout the method of continuity.
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© 2013 Scuola Normale Superiore Pisa
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De Philippis, G. (2013). The Monge-Ampère equation. In: Regularity of Optimal Transport Maps and Applications. Publications of the Scuola Normale Superiore, vol 17. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-458-8_2
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DOI: https://doi.org/10.1007/978-88-7642-458-8_2
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-456-4
Online ISBN: 978-88-7642-458-8
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