Eigenvalues of polyharmonic operators on variable domains

Davide Buoso; Pier Domenico Lamberti

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 4, page 1225-1235
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Buoso, Davide, and Lamberti, Pier Domenico. "Eigenvalues of polyharmonic operators on variable domains." ESAIM: Control, Optimisation and Calculus of Variations 19.4 (2013): 1225-1235. <http://eudml.org/doc/272790>.

@article{Buoso2013,
abstract = {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.},
author = {Buoso, Davide, Lamberti, Pier Domenico},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {polyharmonic operators; eigenvalues; domain perturbation},
language = {eng},
number = {4},
pages = {1225-1235},
publisher = {EDP-Sciences},
title = {Eigenvalues of polyharmonic operators on variable domains},
url = {http://eudml.org/doc/272790},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 4
SP - 1225
EP - 1235
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.
LA - eng
KW - polyharmonic operators; eigenvalues; domain perturbation
UR - http://eudml.org/doc/272790
ER -

References

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