Eigenvalues of poly-harmonic operators on variable domains
Spectral Theory
2012-10-15 v2
Abstract
We consider a class of eigenvalue problems for poly-harmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frech\'{e}t differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove that balls are critical domains.
Cite
@article{arxiv.1205.0948,
title = {Eigenvalues of poly-harmonic operators on variable domains},
author = {Davide Buoso and Pier Domenico Lamberti},
journal= {arXiv preprint arXiv:1205.0948},
year = {2012}
}