Hostname: page-component-7bb8b95d7b-2h6rp Total loading time: 0 Render date: 2024-10-02T18:24:24.936Z Has data issue: false hasContentIssue false
  • English
  • Français

Another approach to a non-elliptic boundary problem

Published online by Cambridge University Press:  22 January 2016

Yoshio Kato
Yoshio Kato*
Affiliation:
Department of Engineering Mathematics Faculty of EngineeringNagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Ω be a bounded domain in ndimensional Euclidian space Rn(n ≧ 2)with C∞boundary Γ of dimension n— 1 and let there be given two real-valued C∞–functions α, β on Γ such that α≧ 0, β ≧ 0and α + β = lthroughout Γ.Then we consider the non-elliptic boundary value problem with λ ≧ 0 (which is always assumed, and in particular when λ =0, we further assume β ≢ 0,throughout this paper) :

(1)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 66 , May 1977 , pp. 13 - 22
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Hayashida, K., On the singular boundary value problem for elliptic equations, Trans. Amer. Math. Soc, 184 (1973), 205–221.CrossRefGoogle Scholar
[2] Hörmander, L., Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math., 83 (1966), 129–209.CrossRefGoogle Scholar
[3] Kaji, A., On the degenerate oblique derivative problems, Proc. Japan Acad., 50 (1974), 1–5.Google Scholar
[4] Kato, Y., Mixed-type boundary conditions for second order elliptic differential equations, J. Math. Soc. Japan, 26 (1974), 405–432.CrossRefGoogle Scholar
[5] Kato, Y., On a class of non-elliptic boundary problems, Nagoya Math. J., 54 (1974), 7–20.CrossRefGoogle Scholar
[6] Taira, K., On some noncoercive boundary value problems for the Laplacian, Proc. Japan Acad., 51 (1975), 141–146.Google Scholar