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The Monge—Ampère Equation by Cristian E Gutierrez
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The Monge—Ampère Equation

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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.
Release date Australia
October 23rd, 2012
Audience
  • Professional & Vocational
Edition
Softcover reprint of the original 1st ed. 2001
Illustrations
XI, 132 p.
Pages
132
Dimensions
156x234x8
ISBN-13
9781461266563
Product ID
21280595

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