By Nam Q. Le,Hiroyoshi Mitake,Hung V. Tran
Consisting of 2 elements, the 1st a part of this quantity is an primarily self-contained exposition of the geometric points of neighborhood and international regularity concept for the Monge–Ampère and linearized Monge–Ampère equations. As an software, we clear up the second one boundary worth challenge of the prescribed affine suggest curvature equation, which are considered as a coupling of the latter equations. Of curiosity in its personal correct, the linearized Monge–Ampère equation additionally has deep connections and functions in research, fluid mechanics and geometry, together with the semi-geostrophic equations in atmospheric flows, the affine maximal floor equation in affine geometry and the matter of discovering Kahler metrics of continuing scalar curvature in advanced geometry.
Among different issues, the second one half offers an intensive exposition of the massive time habit and discounted approximation of Hamilton–Jacobi equations, that have acquired a lot consciousness within the final twenty years, and a brand new method of the topic, the nonlinear adjoint process, is brought. The appendix deals a brief creation to the idea of viscosity ideas of first-order Hamilton–Jacobi equations.
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Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: VIASM 2016 (Lecture Notes in Mathematics) by Nam Q. Le,Hiroyoshi Mitake,Hung V. Tran