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On the Lp bound for degenerate elliptic operators with two variables in the ill posed problem1)

Published online by Cambridge University Press:  22 January 2016

Nobuo Hasesaka  and
Kazuya Hayasida
Nobuo Hasesaka
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa, 920, Japan
Kazuya Hayasida
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa, 920, Japan
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Let Ω be an open set in the upper half plane {y > 0}, whose boundary is denoted by ∂Ω. Let ∂Ω contain an open segment Γ lying on the x-axis.

We consider the following system of first order degenerating on y = 0:

where kj, μj are real constants and bjk are in L∞(Ω), further kj are non-negative integers.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 87 , November 1982 , pp. 261 - 271
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

Footnotes

1)

This work has been supported by Grant-in-Aid for Co-operative Research A organized by the Ministry of Education, the Japanese Government.

References

[1] Carleman, T., Sur un probleme d’unicité pour les systèmes d’équations aux dérivées partielles à deux variables indépendentes, Arkiv Mat., 26B (1938), 1–9.Google Scholar
[2] John, F., Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math., 13 (1960), 551–585.CrossRefGoogle Scholar
[3] Payne, L. E. and Sather, D., On some improperly posed problems for the Chaplygin equation, J. Math. Anal. Appl., 19 (1967), 67–77.CrossRefGoogle Scholar
[4] Saut, J. C. and Scheurer, B., Un théorème de prolongement unique pour des opérateurs elliptiques dont les coefficients ne sont pas localement bornés, C. R. Acad. Sci. Paris, 290 (1980), 595–598.Google Scholar