The Monge-Ampère Equation: 89 - Brossura

Gutiérrez, Cristian E.

Brossura

ISBN 10: 3319828061 ISBN 13: 9783319828060

Casa editrice: Birkhäuser, 2018

Riassunto

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.

Su questo libro

Informazioni sull?autore

Cristian Gutierrez is a Professor in the Department of Mathematics at Temple University in Philadelphia, PA, USA. He teaches courses in Partial Differential Equations and Analysis.

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 3319828061
• ISBN 13: 9783319828060
• Rilegatura: Copertina flessibile
• Numero di pagine: 232
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile