Dynamical and geometric aspects of HamiltonJacobi and linearized MongeAmpere equations : VIASM 2016 / [edited by] Nam Q. Le, Hiroyoshi Mitake and Hung V. Tran.
Contributor(s): Le Nam Q [editor]  Mitake, Hiroyoshi [editor]  Tran, Hung V [editor].
Series: Lecture notes in mathematics ; 2183.Publisher: Cham : Springer, 2017Description: vii, 228 pages : illustrations ; 24 cm.ISBN: 9783319542072.Subject(s): HamiltonJacobi equations  Congresses  MongeAmpere equations  CongressesDDC classification: 515.353Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

515.353 L563 (Browse shelf)  Available  138232 
1. The Affine Bernstein and boundary value problems 
2. The Linearzed MongAmpere equation 
3. The MongeAmpere equation 
4. Ergodic problems for HamiltonJacobi equations 
5. Large time asymptotics of HamiltonJacobi equations 
6. Selection problems in the discounted approximation procedure 
7. Appendix of part II.
Consisting of two parts, the first part of this volume is an essentially selfcontained exposition of the geometric aspects of local and global regularity theory for the MongeAmpère and linearized MongeAmpère 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 MongeAmpère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semigeostrophic 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 HamiltonJacobi 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 firstorder HamiltonJacobi equations.
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