TY - JOUR
T1 - Eigenvalues of polyharmonic operators on variable domains
AU - Buoso, Davide
AU - Lamberti, Pier Domenico
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Domain perturbation
KW - Eigenvalues
KW - Polyharmonic operators
UR - http://www.scopus.com/inward/record.url?scp=84887284179&partnerID=8YFLogxK
U2 - 10.1051/cocv/2013054
DO - 10.1051/cocv/2013054
M3 - Article
SN - 1292-8119
VL - 19
SP - 1225
EP - 1235
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
IS - 4
ER -