Eigenvalues of polyharmonic operators on variable domains
ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 4, pp. 1225-1235.

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.

DOI: 10.1051/cocv/2013054
Classification: 35J40, 35B20, 35P15
Keywords: polyharmonic operators, eigenvalues, domain perturbation
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Buoso, Davide; Lamberti, Pier Domenico. Eigenvalues of polyharmonic operators on variable domains. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 4, pp. 1225-1235. doi : 10.1051/cocv/2013054. http://archive.numdam.org/articles/10.1051/cocv/2013054/

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