"Calculus of Variations and Optimal Control; Optimization" . "Differential geometry" . . . "Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Amp\u00E8re equations, VIASM 2016" . "Text" . . "Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Amp\u00E8re equations, VIASM 2016" . "Hamilton-Jacobi, \u00C9quations de" . . . . "Actes de congr\u00E8s" . "Partial Differential Equations" . . . . "2017" . . . "Partial differential equations" . . "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\u2013Amp\u00E8re and linearized Monge\u2013Amp\u00E8re 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\u2013Amp\u00E8re 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\u2013Jacobi 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\u2013Jacobi equations. ." . . "Calculus of variations" . "Differential Geometry" . "Monge-Amp\u00E8re, \u00C9quations de" .