Analyticity and criticality results for the eigenvalues of the biharmonic operator
Spectral Theory
2016-03-10 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1603.02923,
title = {Analyticity and criticality results for the eigenvalues of the biharmonic operator},
author = {Davide Buoso},
journal= {arXiv preprint arXiv:1603.02923},
year = {2016}
}
Comments
To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 2015