Contact us on (02) 8445 2300
For all customer service and order enquiries

Woodslane Online Catalogues

9781470474201 Academic Inspection Copy

Analysis of Monge-Ampere Equations

  • ISBN-13: 9781470474201
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Nam Q. Le
  • Price: AUD $347.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 16/07/2024
  • Format: Hardback (254.00mm X 178.00mm) 589 pages Weight: 563g
  • Categories: Differential calculus & equations [PBKJ]
Description
Author
Biography
Table of
Contents
Google
Preview
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.
Nam Q. Le, Indiana University, Bloomington, IN
Introduction Geometric and analytic preliminaries The Monge-Ampere equation: Aleksandrov solutions and maximum principles Classical solutions Sections and interior first derivative estimates Interior second derivative estimates Viscosity solutions and Liouville-type theorems Boundary localization Geometry of boundary sections Boundary second derivative estimates Monge-Ampere eigenvalue and variational method The linearized Monge-Ampere equation: Interior Harnack inequality Boundary estimates Green's function Divergence form equations Bibliography Index.
Google Preview content