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Hypoelliptic Overdetermined Systems with Variable Coefficients

Published online by Cambridge University Press:  22 January 2016

Yoshiaki Hashimoto
Yoshiaki Hashimoto*
Affiliation:
Nagoya University
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Let

(1) p(x,D)u = f

be a system of partial difierential equations. We shall say that p (x,D) is hypoelliptic if the distribution solution u is in C∞ wherever f∈C∞ (cf. section 2, Definition 5.)

Here we shall give a sufficient condition for the hypoellipticity of overdetermined systems with variable coefficients.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 41 , February 1971 , pp. 7 - 17
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Hörmander, L.: Differentiability properties of solutions of systems of differential equations, Ark. f. Math. 3 (1958), 527–535.Google Scholar
[2] Hörmander, L.; Pseudo-differential operators and hypoelliptic equations, Proceedings of Symposia in Pure Math. Vol. 10 (1968), 138–183.Google Scholar
[3] Kato, Y.: Sur les systèmes differentiels hypoelliptiques à coefficients variables, Publ. RIMS, Kyoto Univ. Ser. A, Vol. 3 (1968), 351–359.CrossRefGoogle Scholar
[4] Komatsu, H.: On interior regularities of the solutions of principally elliptic systems of linear partial differential equations, J. Fac. Sci. Univ. Tokyo, 141–164 (1961).Google Scholar
[5] Lech, C.: A metric property of the zeros of a complex polynomial ideal, Ark. Math. 3 (1958), 543–554.Google Scholar
[6] Malgrange, B.: Sur les systèmes différentiels à coefficients constants (Suite), Sem. J. Leray (1961/62) n°8.Google Scholar
[7] Matsuura, S.: On general systems of partial differential operators with constant coefficients, J. Math. Soc. Japan, 13 (1961), 94–103.CrossRefGoogle Scholar
[8] Volevic, L.R.: Hypoelliptic systems with variable coefficients, Soviet Math. Dokl. 5 (1964), 797–800.Google Scholar