Generic differentiability of locally Lipschitz functions on product spaces

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 characteri...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1995-12, Vol.52 (3), p.487-498
Main Author: Giles, J.R.
Format: Article
Language:English
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Summary: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.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700014969