JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
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The Gateau derivative of cost functions in the optimal shape problems and the existence of the shape derivatives of solutions of the Stokes problems
Satoshi Kaizu
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2009 Volume 1 Pages 17-20

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Abstract

In optimal shape problems the derivatives of costs with respect to shapes are important, because it gives a direction of lower cost from an initial shape. The differentiability of costs strongly depends on shape derivatives of solutions of mechanical problems, stationary linearized flow problems, the Stokes problems. The shape derivatives are usually given automatically by the associated material derivatives. We show the convergence of shape difference quotients under sufficient conditions. These conditions are applied to the existence of the shape derivatives of the velocity and the pressure in the Stokes problems.

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© 2009 The Japan Society for Industrial and Applied Mathematics
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