{"product_id":"dynamical-and-geometric-aspects-of-hamilton-jacobi-and-linearized-monge-ampere-equations-viasm-2016-9783319542072","title":"Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: Viasm 2016","description":"\u003cp\u003e • Author(s): Hiroyoshi Mitake\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Differential Equations - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eConsisting 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. \u003c\/p\u003e \u003cp\u003eAmong 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.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45274343374999,"sku":"9783319542072","price":2791.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783319542072.webp?v=1769279707","url":"https:\/\/atlanticbooks.com\/products\/dynamical-and-geometric-aspects-of-hamilton-jacobi-and-linearized-monge-ampere-equations-viasm-2016-9783319542072","provider":"Atlantic Books","version":"1.0","type":"link"}