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Generic differentiability of locally Lipschitz functions on product spaces

Published online by Cambridge University Press:  17 April 2009

J.R. Giles
J.R. Giles
Affiliation:
Department of MathematicsThe University of NewcastleNew South Wales 2308Australia
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Abstract

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Although it is known that locally Lipschitz functions are densely differentiable on certain classes of Banach spaces, it is a minimality condition on the subdifferential mapping of the function which enables us to guarantee that the set of points of differentiability is a residual set. We characterise such minimality by a quasi continuity property of the Dini derivatives of the function and derive sufficiency conditions for the generic differentiability of locally Lipschitz functions on a product space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 3 , December 1995 , pp. 487 - 498
Copyright
Copyright © Australian Mathematical Society 1995

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