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Sept 2003 FINITE DIMENSIONAL REDUCTION FOR THE POSITIVITY OF SOME SECOND SHAPE DERIVATIVES
ANTOINE HENROT, MOUNIR RIHANI, MICHEL PIERRE Sinkovics
Methods Appl. Anal. 10(3): 457-476 (Sept 2003).

Abstract

We study the positivity of the second shape derivative around an equilibrium for a functional defined on exterior domains in the plane and which involves the perimeter of the domains and their Dirichlet energy under volume constraint. We prove that small analytic perturbations of circles may be stable or not, depending on the positivity of a simple and explicit two-variable quadratic form. The approach is general and involves a numerical criterion of independent interest for the positivity of a quadratic form on a given hyperplane.

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ANTOINE HENROT. MOUNIR RIHANI. MICHEL PIERRE Sinkovics. "FINITE DIMENSIONAL REDUCTION FOR THE POSITIVITY OF SOME SECOND SHAPE DERIVATIVES." Methods Appl. Anal. 10 (3) 457 - 476, Sept 2003.

Information

Published: Sept 2003
First available in Project Euclid: 21 June 2004

zbMATH: 1068.49031
MathSciNet: MR2059945

Rights: Copyright © 2003 International Press of Boston

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Vol.10 • No. 3 • Sept 2003
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