Name: Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: Viasm 2016 (Lecture Notes in Mathematics) (en Inglés)
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Author: Nam Q. Le
ISBN: 9783319542072

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portada Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: Viasm 2016 (Lecture Notes in Mathematics) (en Inglés)

Formato

Libro Físico

Editorial

Springer

Autor

Nam Q. Le

Año

2017

Idioma

Inglés

N° páginas

240

Encuadernación

Tapa Blanda

ISBN13

9783319542072

N° edición

Categorías

Cálculo

Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: Viasm 2016 (Lecture Notes in Mathematics) (en Inglés)

Nam Q. Le (Autor) · Springer · Tapa Blanda

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Reseña del libro "Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: Viasm 2016 (Lecture Notes in Mathematics) (en Inglés)"

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.