Overview
- Covers the latest advances in the study of the Monge-Ampère equation and its applications
- Includes new chapters on the Harnack inequality for the linearized Monge-Ampère equation and on interior Hölder estimates for second derivatives
- Bibliographic notes provided at the end of each chapter for further exploration of topics
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 89)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
Now in its second edition, this monograph explores the Monge-Ampère 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-Ampère equation and a chapter on interior Hölder 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-Ampère-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.
Reviews
Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Monge-Ampère Equation
Authors: Cristian E. Gutiérrez
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-319-43374-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing 2016
Hardcover ISBN: 978-3-319-43372-1Published: 02 November 2016
Softcover ISBN: 978-3-319-82806-0Published: 16 June 2018
eBook ISBN: 978-3-319-43374-5Published: 22 October 2016
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 2
Number of Pages: XIV, 216
Number of Illustrations: 3 b/w illustrations, 3 illustrations in colour
Topics: Partial Differential Equations, Differential Geometry, Mathematical Applications in the Physical Sciences