Analysis of Monge-Ampere Equations - Couverture souple

Le, Nam Q.

Couverture souple

ISBN 10 : 1470476258 ISBN 13 : 9781470476250

Editeur : American Mathematical Society, 2024

Synopsis

This book presents a systematic analysis of the Monge-Ampere equation, the linearized Monge-Ampere equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge-Ampere equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations. The modern treatment of boundary behaviors of solutions to Monge-Ampere equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Holder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas. This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject.

A propos du livre

À propos de l'auteur

Nam Q. Le, Indiana University, Bloomington, IN

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2024
• Langue: anglais
• ISBN 10: 1470476258
• ISBN 13: 9781470476250
• Reliure: Broché
• Nombre de pages: 227
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible