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The Range of the Gradient of a Continuously Differentiable Bump

Borwein, Jonathan M. and Fabian, Marian and Kortezov, Ivaylo and Loewen, Philip D. (2001) The Range of the Gradient of a Continuously Differentiable Bump. J. Nonlinear and Convex Analysis, 2 . pp. 1-19.

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      Abstract

      For a continuously differentiable function with bounded nonempty support,the range of the gradient cannot be locally contained in a hyperplane.However, iterative methods allow the construction of continuously differentiable functions whose gradient ranges have rather general topological features.For example, the gradient range may fail to be simply connected.

      Item Type: Article
      Additional Information: pubdom FALSE
      Subjects: 46-xx Functional analysis > 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
      58-xx Global analysis, analysis on manifolds > 58Cxx Calculus on manifolds; nonlinear operators
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 28 Sep 2014 14:41
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/231

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