@inbook{91c9ff11abb543e8adeca63fde13d9d2,
title = "On a Classical Spectral Optimization Problem in Linear Elasticity",
abstract = "We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the N-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam{\'e} and the Reissner–Mindlin systems.",
keywords = "Domain perturbation, Eigenvalues, Polyharmonic operators",
author = "Davide Buoso and Lamberti, {Pier Domenico}",
note = "Publisher Copyright: {\textcopyright} 2015, Springer International Publishing Switzerland.",
year = "2015",
doi = "10.1007/978-3-319-17563-8_3",
language = "English",
series = "International Series of Numerical Mathematics",
publisher = "SPRINGER",
pages = "43--55",
booktitle = "International Series of Numerical Mathematics",
}