Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems

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概要

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• We consider the Dirichlet and the Neumann eigenvalue problem for the Laplace operator on a variable nonsmooth domain, and we prove that the elementary symmetric functions of the eigenvalues splitting from a given eigenvalue upon domain deformation have a critical point at a domain with the shape of a ball. Correspondingly, we formulate overdetermined boundary value problems of the type of the Schiffer conjecture.

• 社団法人 日本数学会の論文
• 2006-01-01

著者

• Lanza De

  Dipartimento Di Matematica Pura Ed Applicata Universita Di Padova

• LAMBERTI Pier

  Dipartimento di Matematica Pura ed Applicata Universita di Padova

関連論文

• Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems
• Differentiability properties of some nonlinear operators associated to the conformal welding of Jordan curves in Schauder spaces

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