Eigenvalues of poly-harmonic operators on variable domains
By Davide Buoso, Pier Domenico Lamberti. 2012
48 citations recorded by the source corpus.
We consider a class of eigenvalue problems for poly-harmonic oper- ators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenval- ues upon domain perturbations and compute Hadamard-type formulas for the Frechet 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/956f81a60c4abde01d56f3dcbb6b0bad5213265b
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- A few shape optimization results for a biharmonic Steklov problem (2015, background): “We also refer to [12, 13] where the authors prove analyticity properties in the spirit of [31] for Dirichlet and intermediate boundary conditions respectively, and show that balls are critical domains for all the elementary symmetric functions of the eigenvalues.”