Lecture Notes in Mathematics

Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations

VIASM 2016

Authors: Le, Nam, Mitake, Hiroyoshi, Tran, Hung

Editors: Mitake, Hiroyoshi, Tran, Hung (Eds.)

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  • Contains a gentle introduction to Monge-Ampère equations
    Offers a starting point to learn the theory of viscosity solutions (see appendix of part 2)
    Provides up-to-date research directions in the fields of Hamilton-Jacobi and linearized Monge-Ampere equations

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About this book

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry.  

Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton–Jacobi equations.

 

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-54208-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $49.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations
Book Subtitle
VIASM 2016
Authors
Editors
  • Hiroyoshi Mitake
  • Hung Tran
Series Title
Lecture Notes in Mathematics
Series Volume
2183
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-54208-9
DOI
10.1007/978-3-319-54208-9
Softcover ISBN
978-3-319-54207-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VII, 228
Number of Illustrations
15 b/w illustrations, 1 illustrations in colour
Topics