@inproceedings{c0249901834042278b3a9f2bbe4ec5c4,
title = "Analyticity and criticality results for the eigenvalues of the biharmonic operator",
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 = "Biharmonic operator, Boundary value problems, Eigenvalues, Hadamard formulas, Isovolumetric perturbations, Perturbations, Plates, Shape criticality, Steklov",
author = "Davide Buoso",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE{\textquoteright}s, GPPEPDEs 2015 ; Conference date: 25-05-2015 Through 29-05-2015",
year = "2016",
doi = "10.1007/978-3-319-41538-3_5",
language = "English",
isbn = "9783319415369",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "65--85",
editor = "Carlo Nitsch and Filippo Gazzola and Kazuhiro Ishige and Paolo Salani",
booktitle = "Geometric Properties for Parabolic and Elliptic PDE{\textquoteright}s - GPPEPDEs 2015",
}