Monge-Ampere Equation

English

Series: Progress in Nonlinear Differential Equations and Their Applications Ser.

Volume: Vol. 44

ISBN: 0817641777

EAN: 9780817641771

Category: Mathematics / Differential Equations

Publisher: Birkhauser Boston

Release Date: 10/07/2011

Synopsis: The classical Monge-Amp??re equation has been the center of considerable interest in recent years because of its important role in several areas of applied mathematics. In reflecting these developments, this works stresses the geometric aspects of this beautiful theory, using some techniques from harmonic analysis---covering lemmas and set decompositions. Moreover, Monge-Amp??re type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem.The book is an essentially self-contained exposition of the theory of weak solutions, including the regularity results of L.A. Caffarelli. The presentation unfolds systematically from introductory chapters, and an effort is made to present complete proofs of all theorems. Included are examples, illustrations, bibliographical references at the end of each chapter, and a comprehensive index.Topics covered include: * Generalized Solutions * Non-divergence Equations * The Cross-Sections of Monge-Amp??re * Convex Solutions of D^2u = 1 in R^n * Regularity Theory * W^2, p Estimates The Monge-Amp??re Equation is a concise and useful book for graduate students and researchers in the field of nonlinear equations.

Excerpt: Unknown Property Excerpt

Monge-Ampere Equation

Illustrated: Yes

Format: Hardcover

Width: 6.1 inches

Length: 9.25 inches

Weight: 11.99 oz

Pages: LXXX, 127