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On the Eigenvalues of a Biharmonic Steklov Problem

In: Integral Methods in Science and Engineering

Author

Listed:
  • D. Buoso

    (Politecnico di Torino)

  • L. Provenzano

    (University of Padova)

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.

Suggested Citation

  • D. Buoso & L. Provenzano, 2015. "On the Eigenvalues of a Biharmonic Steklov Problem," Springer Books, in: Christian Constanda & Andreas Kirsch (ed.), Integral Methods in Science and Engineering, edition 1, chapter 0, pages 81-89, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-16727-5_7
    DOI: 10.1007/978-3-319-16727-5_7
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