Hamilton-Jacobi Equations in Infinite Dimensions

Download or read book Hamilton-Jacobi Equations in Infinite Dimensions written by Michael G. Crandall and published by . This book was released on 1986 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with a number of topics in the theory of viscosity solutions of Hamilton Jacobi equations in infinite dimensional spaces. The development of the theory in the generality in which the space or state variable lies in an infinite dimensional space is partly motivated by the hope of eventual applications to the theory of control of partial differential equations or control under partial observation. Among the results presented are: The existence and uniqueness theory previously discussed in spaces with the Radon Nikodym property is extended beyond this class; examples are given which show that Galerkin approximation arguments in their naive forms cannot be made the basis of an existence theory; some equations with unbounded terms of the sort that arise in control of pde's are treated by means of a change of variables reducing the problem to the previously studied cases. Keywords: Viscosity solutions; Hamilton Jacobi equations.