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Analysis of Monge–Ampère Equations by Le, Nam Q. is a nonfiction available to read on EtoBox.

What is Analysis of Monge–Ampère Equations about?

This book presents a systematic analysis of the Monge–Ampère equation, the linearized Monge–Ampère 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–Ampère 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–Ampère 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 Hölder 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 w

Who reads Analysis of Monge–Ampère Equations?

Author

Le, Nam Q.

Publisher

American Mathematical Society [AMS]

Published

2024

Language

EN

ISBN

9781470476250

Category

nonfiction

Subjects

Mathematics, Differential Equations, Stem