Existence of Viscosity Solutions of Hamilton-Jacobi Equations.

摘要

Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations, control theory and differential games. However, nonlinear first order partial differential equations almost never have global classical solutions, and one must deal with generalized solutions. Recently M. G. Crandall and P. L. Lions introduced the class of viscosity solutions of these equations and proved uniqueness within this class. This paper discusses the existence of these solutions under assumptions closely related to the ones which guarantee the uniqueness.