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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
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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.
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- Research Article
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- 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
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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
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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
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