The Monge-Ampere Equation (Paperback, Softcover reprint of the original 2nd ed. 2016)

Now in its second edition, this monograph explores the Monge-Ampere equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples and exercises are offered to further illustrate important concepts. Some of the topics considered include generalized solutions, non-divergence equations, cross sections, and convex solutions. New to this edition is a chapter on the linearized Monge-Ampere equation and a chapter on interior Hoelder estimates for second derivatives. Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Ampere-type equations and their diverse applications in the areas of differential geometry, the calculus of variations, optimization problems, optimal mass transport, and geometric optics. Both researchers and graduate students working on nonlinear differential equations and their applications will find this to be a useful and concise resource.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Progress in Nonlinear Differential Equations and Their Applications, 89
Release date:	June 2018
First published:	2016
Authors:	Cristian E. Gutierrez
Dimensions:	235 x 155 x 12mm (L x W x T)
Format:	Paperback
Pages:	216
Edition:	Softcover reprint of the original 2nd ed. 2016
ISBN-13:	978-3-319-82806-0
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling
LSN:	3-319-82806-1
Barcode:	9783319828060

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