Hamilton-Jacobi Equations in Infinite Dimensions. Part 3.
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1986
- Accession Number
- ADA167521
Entities
People
- Michael G. Crandall
- Pierre-louis Lions
Organizations
- University of Wisconsin–Madison