Proceedings of the Japan Academy, Series A, Mathematical Sciences

Spectra of the Laplacian with small Robin conditional boundary

Shin Ozawa

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 72, Number 3 (1996), 53-54.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195510417

Digital Object Identifier
doi:10.3792/pjaa.72.53

Mathematical Reviews number (MathSciNet)
MR1391896

Zentralblatt MATH identifier
0857.35094

Subjects
Primary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions
Secondary: 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)

Citation

Ozawa, Shin. Spectra of the Laplacian with small Robin conditional boundary. Proc. Japan Acad. Ser. A Math. Sci. 72 (1996), no. 3, 53--54. doi:10.3792/pjaa.72.53. https://projecteuclid.org/euclid.pja/1195510417


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References

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  • [2] S. Ozawa: Electrostatic capacity and eigenvalues of the Laplacian. J. Fac. Sci. Univ. Tokyo., 30, 53-62 (1983).
  • [3] S. Ozawa: Spectra of domains with small spherical Neumann boundary. J. Fac. Sci. Univ. Tokyo, 30, 259-277 (1983).
  • [4] S. Ozawa : Singular variation of the ground state eigenvalue for a semilinear elliptic equation. Tohoku Math. J., 45, 359-368 (1993).
  • [5] S. Ozawa: Singular Hadamard's variation of domains and eigenvalues of the Laplacian. II. Proc. Japan Acad., 57A, 242-246 (1981).
  • [6] S. Ozawa: An asymptotic formula for the eigenvalue of the Laplacian in a three dimensional domain with a small hole. J. Fac. Sci. Univ. Tokyo, Sect. IA, 30, 53-62 (1983).
  • [7] S. Ozawa and S. Roppongi: Singular variation of domain and spectre of the Laplacian with small Robin conditional boundary. II. Kodai Math. J., 15, 403-429 (1992).
  • [8] S. Roppongi: Asymptotic of eigenvalues of the Laplacian with small spherical Robin boundary. Osaka J. Math., 30, 783-811 (1993).