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A generalization of a theorem of Barron and Jensen and a comparison theorem for lower semicontinuous viscosity solutions

Published online by Cambridge University Press:  11 July 2007

Hitoshi Ishii
Hitoshi Ishii
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan (hishii@comp.metro-u.ac.jp)
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Abstract

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We extend and clarify some of observations due to Barron and Jensen concerning the relation between subdifferentials and superdifferentials of a function and extend the comparison principle for semicontinuous solutions of Hamilton–Jacobi equations with convex Hamiltonians to that in infinite-dimensional Hilbert spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 1 , February 2001 , pp. 137 - 154
Copyright
Copyright © Royal Society of Edinburgh 2001