Proceedings of the Japan Academy, Series A, Mathematical Sciences

Characterization of the eigenfunctions in the singularly perturbed domain

Shuichi Jimbo

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 63, Number 8 (1987), 285-288.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195513562

Digital Object Identifier
doi:10.3792/pjaa.63.285

Mathematical Reviews number (MathSciNet)
MR931237

Zentralblatt MATH identifier
0659.35076

Subjects
Primary: 35P05: General topics in linear spectral theory
Secondary: 35B40: Asymptotic behavior of solutions 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]

Citation

Jimbo, Shuichi. Characterization of the eigenfunctions in the singularly perturbed domain. Proc. Japan Acad. Ser. A Math. Sci. 63 (1987), no. 8, 285--288. doi:10.3792/pjaa.63.285. https://projecteuclid.org/euclid.pja/1195513562


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References

  • [1] J. T. Beale: Scattering" frequencies of resonators. C.P.A.M., XXVI, 549-563 (1973).
  • [2] S. Jimbo: Singular perturbation of domains and semilinear elliptic equation (to appear in J. Fac. Sci. Univ. Tokyo).
  • [3] S. Jimbo: Singular perturbation of domains and semilinear elliptic equation. II (preprint).
  • [4] S. Kaizu: Upper semicontinuity of eigenvalues of self ad joint operators defined on moving domains. Proc. Japan Acad., 61A, 243-245 (1985).

See also

  • Part II: Shuichi Jimbo. Characterization of the eigenfunctions in the singularly perturbed domain, II. Proc. Japan Acad. Ser. A Math. Sci., Volume 64, Number 1 (1988), 14--16.