| The Monge--Ampère Equation Softcover Repri Edition Contributor(s): Gutierrez, Cristian E. (Author) |
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ISBN: 1461266564 ISBN-13: 9781461266563 Publisher: Birkhauser OUR PRICE: $85.49 Product Type: Paperback Published: October 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - Partial - Medical - Mathematics | Applied |
| Dewey: 515.353 |
| Series: Progress in Nonlinear Differential Equations and Their Appli |
| Physical Information: 0.32" H x 6.14" W x 9.21" (0.48 lbs) 132 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: In recent years, the study of the Monge-Ampere equation has received consider- able attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to reflect these advances in an essentially self-contained systematic exposi- tion of the theory of weak: solutions, including recent regularity results by L. A. Caffarelli. The theory has a geometric flavor and uses some techniques from har- monic analysis such us covering lemmas and set decompositions. An overview of the contents of the book is as follows. We shall be concerned with the Monge-Ampere equation, which for a smooth function u, is given by (0.0.1) There is a notion of generalized or weak solution to (0.0.1): for u convex in a domain n, one can define a measure Mu in n such that if u is smooth, then Mu 2 has density det D u. Therefore u is a generalized solution of (0.0.1) if M u = f. |