Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity

Title: Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity
Creator: Borwein, Jonathan M.; Zhu, Qiji J.
Relation: SIAM Journal on Control and Optimization Vol. 34, Issue 5, p. 1568-1591
Publisher Link: http://dx.doi.org/10.1137/S0363012994268801
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Resource Type: journal article
Date: 1996
Description: 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.
Subject: viscosity subderivative; fuzzy sum rule; viscosity solutions; Hamilton–Jacobi equations; smooth spaces; metric regularity
Identifier: http://hdl.handle.net/1959.13/940477
Identifier: uon:13018
Identifier: ISSN:0363-0129
Language: eng
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