- Title
- Lipschitz functions with prescribed derivatives and subderivatives
- Creator
- Borwein, Jonathan M.; Moors, Warren B.; Wang, Xianfu
- Relation
- Nonlinear Analysis: Theory, Methods & Applications Vol. 29, Issue 1, p. 53-63
- Publisher Link
- http://dx.doi.org/10.1016/S0362-546X(96)00050-8
- Publisher
- Pergamon
- Resource Type
- journal article
- Date
- 1997
- Description
- It is natural to ask when a given set-valued mapping T, which maps from a nonempty open subset U of a Banach space X into subsets of its dual, is the Clarke subdifferential mapping of some real-valued locally Lipschitz functions defined on U. In the case when X = R and U is an open interval the answer is known (see [l]). However, the general question still remains. Even the simpler question of how to construct nontrivial Lipschitz functions which are not built-up from either convex or distance functions has yet to be satisfactorily resolved. In this paper we present a technique for constructing such real-valued locally Lipschitz functions defined on separable Banach spaces. Using this construction we are able to recreate many known examples of pathological locally Lipschitz functions.
- Subject
- Lipschitz functions; differentiability; Clarke subgradient; minimal cusco; Haar null set; maximal cyclically monotone operator
- Identifier
- http://hdl.handle.net/1959.13/1046791
- Identifier
- uon:14689
- Identifier
- ISSN:0362-546X
- Language
- eng
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