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On a hypoelliptic boundary value problem

Published online by Cambridge University Press:  22 January 2016

Tadato Matsuzawa*
Affiliation:
Department of Mathematics, Nagoya University
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This paper is devoted to the investigation of the hypoellipticity of the following first boundary value problem:

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Hörmander, L.: Linear partial differential operators, Springer Verlag, 1964.Google Scholar
[2] Hörmander, L.: Hypoelliptic second order differential equations, Acta Math., 119 (1968), 147171.Google Scholar
[3] Hörmander, L.: Fourier integral operators, I, Acta Math., 127 (1971), 79183.CrossRefGoogle Scholar
[4] Kato, Y.: On a class of hypoelliptic differential operators, Proc. Japan Acad. 46, No. 1 (1970), 3337.Google Scholar
[5] Matsuzawa, T.: Sur les équations utt+tαuxx=f(α≧0) , Nagoya Math. J., Vol. 42 (1971), 4355.Google Scholar
[6] Matsuzawa, T.: On some degenerate parabolic equations I, Nagoya Math. J. 51 (1973), 5777, II, Nagoya Math. J. 52 (1973), 6184.Google Scholar
[7] Matsuzawa, T. (with Y. Hashimoto): On a class of degenerate elliptic equations, Nagoya Math. J. 55 (1974), 181204.Google Scholar
[8] Mizohata, S.: Solutions nulles et solutions non analytiques, J. Math. Kyoto Univ. (1962), 271302.Google Scholar
[9] Oleinik, O. A. and Radkevič, E. V.: Second order equations with nonnegative characteristic form, Amer. Math. Soc, 1973.Google Scholar
[10] Treves, F.: A new method of proof of the subelliptic estimates, Comm. Pure Applied Math., 24 (1971), 71115.Google Scholar
[11] Treves, F.: Analytic-hypoelliptic partial differential equations of principal type, Comm. Pure Applied Math., 24 (1971), 537570.Google Scholar