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Eigenvalues of polyharmonic operators on variable domains

Published online by Cambridge University Press:  06 September 2013

Davide Buoso  and
Pier Domenico Lamberti
Davide Buoso
Affiliation:
Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste, 63, 35126 Padova, Italy. dbuoso@math.unipd.it; lamberti@math.unipd.it
Pier Domenico Lamberti
Affiliation:
Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste, 63, 35126 Padova, Italy. dbuoso@math.unipd.it; lamberti@math.unipd.it
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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.

Keywords

Polyharmonic operatorseigenvaluesdomain perturbation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 4 , October 2013 , pp. 1225 - 1235
Copyright
© EDP Sciences, SMAI, 2013

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