Analyticity and criticality results for the eigenvalues of the biharmonic operator

Davide Buoso

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arXiv · 1603.02923

Analyticity and criticality results for the eigenvalues of the biharmonic operator

Davide Buoso

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Abstract

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.

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BibTeX RIS

Davide Buoso. 2016-03-09. Analyticity and criticality results for the eigenvalues of the biharmonic operator. https://arxiv.org/abs/1603.02923

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