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On a class of non-elliptic boundary problems

Published online by Cambridge University Press:  22 January 2016

Yoshio Kato
Yoshio Kato*
Affiliation:
Mathematical Institute, Nagoya University
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Let Ω be a bounded domain in Rl (l ≥ 2) with, C∞ boundary Γ of dimension l — 1 and let there be given a second order elliptic differential equation

(1) in Ω,

where ∂j = ∂/∂xi and all coefficients are assumed, for the sake of simplicity, to be real-valued and C∞ on .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 54 , July 1974 , pp. 7 - 20
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Egorov, V. Ju., Kondrat’ev, V. A., The oblique derivative problem, Mat. Sbornik 78 (1969), 148–176. = Math. USSR Sbornik 7 (1969), 139–169.Google Scholar
[2] Hayashida, K., On the singular boundary value problem for elliptic equations, Trans. Amer. Math. Soc., 184 (1973), 205–221.Google Scholar
[3] Kato, Y., Mixed-type boundary conditions for second order elliptic differential equations, to appear in J. Math. Soc. Japan 26 (1974).Google Scholar
[4] Mazja, V. G., The degenerate problem with oblique derivative, Uspehi Mat. Nauk 25 (1970), 275–276.Google Scholar