Viscosity Solutions and Viscosity Subderivatives in Smooth Banach Spaces with Applications to Metric Regularity

Authors

Jonathan Borwein, Simon Fraser University
Qiji Jim Zhu, Western Michigan UniversityFollow

Document Type

Article

Publication Date

1996

Abstract

In Gateaux or bornologically differentiable spaces there are two natural generalizations of the concept of a Fréchet subderivative. In this paper we study the viscosity subderivative (which is the more robust of the two) and establish refined fuzzy sum rules for it in a smooth Banach space. These rules are applied to obtain comparison results for viscosity solutions of Hamilton–Jacobi equations in smooth spaces. A unified treatment of metric regularity in smooth spaces completes the paper. This illustrates the flexibility of viscosity subderivatives as a tool for analysis.

Comments

https://doi.org/10.1137/S0363012994268801

WMU ScholarWorks Citation

Borwein, Jonathan and Zhu, Qiji Jim, "Viscosity Solutions and Viscosity Subderivatives in Smooth Banach Spaces with Applications to Metric Regularity" (1996). Math Faculty Publications. 3.
https://scholarworks.wmich.edu/math_pubs/3