Friedlander ’ S Eigenvalue Inequalities and the Dirichlet-to-neumann Semigroup

@inproceedings{Arendt2012FriedlanderS,
  title={Friedlander ’ S Eigenvalue Inequalities and the Dirichlet-to-neumann Semigroup},
  author={Wolfgang Arendt and Rafe Mazzeo},
  year={2012}
}
If Ω is any compact Lipschitz domain, possibly in a Riemannian manifold, with boundary Γ = ∂Ω, the Dirichlet-to-Neumann operator Dλ is defined on L2(Γ) for any real λ. We prove a close relationship between the eigenvalues of Dλ and those of the Robin Laplacian ∆μ, i.e. the Laplacian with Robin boundary conditions ∂νu = μu. This is used to give another proof of the Friedlander inequalities between Neumann and Dirichlet eigenvalues, λk+1 ≤ λk , k ∈ N, and to sharpen the inequality to be strict… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 25 references

On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator

  • N. Filinov
  • St. Petersburg Math. J., 16
  • 2005
Highly Influential
5 Excerpts

Some inequalities between Dirichlet and Neumann eigenvalues

  • L. Friedlander
  • Arch. Rational Mech. Anal., 116
  • 1991
Highly Influential
10 Excerpts

A method of finding the eigenvalues and eigenfunctions of self-adjoint elliptic operators

  • J. P. Grégoire, J. C. Nédélec, J. Planchard
  • Comp. Methods in Appl. Mech. and Eng., 8
  • 1976
Highly Influential
5 Excerpts

Remarks on a paper of L

  • R. Mazzeo
  • Friedlander concerning inequalities between…
  • 1991
Highly Influential
4 Excerpts

Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities

  • F. Gesztesy, M. Mitrea
  • J. Diff. Eq., 247
  • 2009
2 Excerpts

On the comparison of the Dirichlet and Neumann counting functions

  • Y. Safarov
  • “Spectral Theory of Differential Operators: M.Sh…
  • 2008
1 Excerpt

Spectral properties of the Dirichlet-to-Neumann operator on Lipschitz domains

  • W. Arendt, R. Mazzeo
  • Ulmer Seminare, Heft 12
  • 2007
3 Excerpts

An approximating family for the Dirichlet-to-Neumann semigroup

  • H. Emamirad, I. Laadnani
  • Adv. Diff. Equ., 11
  • 2006
1 Excerpt

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