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We consider a class of eigenvalue problems for polyharmonic 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 Frechét 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.
@article{COCV_2013__19_4_1225_0,
author = {Buoso, Davide and Lamberti, Pier Domenico},
title = {Eigenvalues of polyharmonic operators on variable domains},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1225--1235},
publisher = {EDP-Sciences},
volume = {19},
number = {4},
year = {2013},
doi = {10.1051/cocv/2013054},
mrnumber = {3182687},
zbl = {1291.35144},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013054/}
}
TY - JOUR AU - Buoso, Davide AU - Lamberti, Pier Domenico TI - Eigenvalues of polyharmonic operators on variable domains JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1225 EP - 1235 VL - 19 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013054/ DO - 10.1051/cocv/2013054 LA - en ID - COCV_2013__19_4_1225_0 ER -
%0 Journal Article %A Buoso, Davide %A Lamberti, Pier Domenico %T Eigenvalues of polyharmonic operators on variable domains %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1225-1235 %V 19 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013054/ %R 10.1051/cocv/2013054 %G en %F COCV_2013__19_4_1225_0
Buoso, Davide; Lamberti, Pier Domenico. Eigenvalues of polyharmonic operators on variable domains. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1225-1235. doi: 10.1051/cocv/2013054
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