VISCOSITY SOLUTIONS AND VISCOSITY SUBDERIVATIVES IN SMOOTH BANACH-SPACES WITH APPLICATIONS TO METRIC REGULARITY

In Gateaux or bornologically differentiable spaces there are two natur al generalizations of the concept of a Frechet subderivative. In this paper we study the viscosity subderivative (which is the more robust o f the two) and establish refined fuzzy sum rules for it in a smooth Ba nach space. These rules are applied to obtain comparison results for v iscosity solutions of Hamilton-Jacobi equations in smooth spaces. A un ified treatment of metric regularity in smooth spaces completes the pa per. This illustrates the flexibility of viscosity subderatives as a t ool for analysis.