The Monge—Ampère Equation

di Cristian E. Gutierrez (Autore)

Springer-Verlag New York Inc., 2012

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.

• Autore: Cristian E. Gutierrez
• Editore: Springer-Verlag New York Inc.
• Collana: Progress in Nonlinear Differential Equations and Their Applications
• Anno: 2012
• Rilegatura: Paperback / softback
• Pagine: 132 p.
• Dimensioni: 235 x 155 mm
• EAN: 9781461266563

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