We consider an eigenvalue problem for the biharmonic operator with Steklov-type boundary conditions. We obtain it as a limiting Neumann problem for the biharmonic operator in a process of mass concentration at the boundary. We study the dependence of the spectrum upon the domain. We show analyticity of the symmetric functions of the eigenvalues under isovolumetric perturbations and prove that balls are critical points for such functions under measure constraint. Moreover, we show that the ball is a maximizer for the first positive eigenvalue among those domains with a prescribed fixed measure.
On the eigenvalues of a biharmonic Steklov problem / Provenzano, Luigi; Buoso, Davide. - (2015). (Intervento presentato al convegno Integral Methods in Science and Engineering tenutosi a Karlsruhe (Germany)) [10.1007/978-3-319-16727-5_7].
On the eigenvalues of a biharmonic Steklov problem
Luigi Provenzano
;
2015
Abstract
We consider an eigenvalue problem for the biharmonic operator with Steklov-type boundary conditions. We obtain it as a limiting Neumann problem for the biharmonic operator in a process of mass concentration at the boundary. We study the dependence of the spectrum upon the domain. We show analyticity of the symmetric functions of the eigenvalues under isovolumetric perturbations and prove that balls are critical points for such functions under measure constraint. Moreover, we show that the ball is a maximizer for the first positive eigenvalue among those domains with a prescribed fixed measure.| File | Dimensione | Formato | |
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