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

Nam Q. Le

ISBN 10: 3319542079 / ISBN 13: 9783319542072

Edité par Springer International Publishing, Springer International Publishing Jun 2017, 2017

A propos de cet article

Neuware -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 newapproach 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 240 pp. Englisch.

N° de réf. du vendeur 9783319542072

Détails bibliographiques

• Titre: Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations
• Éditeur: Springer International Publishing, Springer International Publishing Jun 2017
• Date de parution: 2017
• Langue: anglais
• ISBN à 10 chiffres: 3319542079
• ISBN à 13 chiffres: 9783319542072
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 14 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 14 millimètres de profondeur
• Poids: 371 grammes

A propos de ce titre

Synopsis

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 newapproach 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.