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Essentially Smooth Lipschitz Functions

Borwein, Jonathan M. and Moors, Warren B. (1997) Essentially Smooth Lipschitz Functions. Journal of Functional Analysis, 149 (2). pp. 305-351.

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      Abstract

      In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on Banach spaces. For example, we examine the relationship between integrability, D-representability and strict differentiability. In addition to this, we show that on a large class of Banach spaces there is a significant family of locally Lipschitz functions which are integrable, D-representable and possess desirable differentiability properties. We also present some striking applications of our results to distance functions.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Lipschitz function, distance function, D-representable, integrable, proximal normal formula, minimal cusco, Haar-null set
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      46-xx Functional analysis > 46Nxx Miscellaneous applications of functional analysis
      52-xx Convex and discrete geometry > 52Axx General convexity
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 13 Sep 2014 21:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/95

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