Viscosity Solutions and Viscosity Subderivatives in Smooth Banach
Spaces with Applications to Metric Regularity
J. Borwein and Q. J. Zhu
Abstract: In Gateaux or bornologically differentiable spaces there are two natural
generalizations of the concept of a Fr\' echet 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.