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A domain perturbation problem for elliptic operators

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Summary

Eigenvalue problems with null boundary data are considered for second order symmetric linear elliptic operators in bounded domains of Euclidean n-space. The main theorems give estimates for the perturbation of the eigenvalues and eigenfunctions under the deformation of attaching an ɛ-handle to the domain. In particular it is proved that the variation of every eigenvalue under such a deformation is of order ϕ(ɛ), where ϕ denotes the reciprocal of the parametrix.

References

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    C. A. Swanson,On spectral estimation, Bull. Amer. Math. Soc.,68 (1962), pp. 33–35.

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Entrata in Redazione il 23 giugno 1976.

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Swanson, C.A. A domain perturbation problem for elliptic operators. Annali di Matematica 114, 229–240 (1977). https://doi.org/10.1007/BF02413788

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Keywords

  • Eigenvalue Problem
  • Bounded Domain
  • Elliptic Operator
  • Boundary Data
  • Domain Perturbation