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Cα estimation on the boundary for the gradient of the shape derivative of a Neumann problem in ℝ3

Published online by Cambridge University Press:  14 November 2011

A. Novruzi
A. Novruzi
Affiliation:
Université Henri Poincaré Nancy 1, Laboratoire de Mathématiques, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France (novruzi@Oiecn.u-nancy.fr)
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Extract

In this paper we establish a non-global Cα estimation on the boundary for the gradient of the solution of a Neumann exterior problem in ℝ3. The boundary data of this problem are with small compact support and with C0 norm tending to infinity when the diameter of support data goes to zero. This problem appears, for instance, in the numerical shape optimization problems when the Newton method is used. It turns out that the gradient decreases when the distance to the boundary data supports increases (Saint Venant's principle), which, when used in applications, leads to a strong reduction of the gradient computational cost.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 6 , 1999 , pp. 1229 - 1250
Copyright
Copyright © Royal Society of Edinburgh 1999

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