Proceedings of the Japan Academy, Series A, Mathematical Sciences

Singular variation of domains and $L^\infty$ boundedness of eigenfunctions for some semi-linear elliptic Equations

Shin Ozawa and Susumu Roppongi

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 70, Number 3 (1994), 67-70.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195511112

Digital Object Identifier
doi:10.3792/pjaa.70.67

Mathematical Reviews number (MathSciNet)
MR1276875

Zentralblatt MATH identifier
0799.35088

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B25: Singular perturbations

Citation

Ozawa, Shin; Roppongi, Susumu. Singular variation of domains and $L^\infty$ boundedness of eigenfunctions for some semi-linear elliptic Equations. Proc. Japan Acad. Ser. A Math. Sci. 70 (1994), no. 3, 67--70. doi:10.3792/pjaa.70.67. https://projecteuclid.org/euclid.pja/1195511112


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References

  • [1] S. S. Lin : Semilinear elliptic equations on singularly pertubed domains. Comm. Partial Differential Equations, 16, 617-645 (1991).
  • [2] S. Ozawa: Singular variation of the ground state eigenvalue for a semilinear elliptic equation. Tohoku Math. J., 45, 359-368 (1993).
  • [3] S. Ozawa: L% boundedness of nonlinear eigenfunction under singular variation of domains (preprint).
  • [4] S. Ozawa: Asymptotic property of an eigenfunction of the Laplacian under singular variation of domains-The Neumann condition. Osaka J. Math., 22, 639-655 (1985).