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Almost hypoelliptic differential operators with variable coefficients

Published online by Cambridge University Press:  24 October 2008

Robert J. Elliott
Robert J. Elliott
Affiliation:
Mathematical Institute, Oxford
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Extract

We have called a linear partial differential operator P almost hypoelliptic in some of the variables if the distribution u is strongly regular in those variables in every open subset where this is true of Pu. In an earlier paper (l) we have characterised almost hypoelliptic operators with constant coefficients. Following techniques of Hörmander (2) and Yoshikawa(5) we obtain in this paper some a priori inequalities for almost hypoelliptic operators and derive results about the solvability of the adjoint operator P*. Our notation for various standard distribution spaces and multi-indices follows Hörmander (2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 287 - 293
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Elliott, R. J.Almost hypoelliptic differential operators. Proc. London Math. Soc. 3, 39 (1969), 537–552.CrossRefGoogle Scholar
(2)Höbmandeb, L.Linear partial differential operators (Springer, Berlin, 1963).Google Scholar
(3)Malgrange, B.Sur une classe d'opeérateurs diffeérentiels hypoelliptiques. Bull. Soc. Math. France, 85 (1957), 283–306.Google Scholar
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(5)Yoshtkawa, A.On the hypoellipticity of differential operators. J. Fac. Sci. Univ. Tokyo, Sect. 1, 14 (1967), 81–88.Google Scholar