- 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
- Full Text
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