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Hypoellipticity for a class of the second order partial differential equations

Published online by Cambridge University Press:  22 January 2016

Tadato Matsuzawa
Tadato Matsuzawa*
Affiliation:
Mathematical Institute, Nagoya University
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In this paper, we shall investigate the hypoellipticity for a class of degenerate equations of the second order with complex coefficients as a direct extension of the results obtained in [8]. As is well known, the satisfactory general results about hypoellipticity of real operators of the second order have been obtained in [3] and [9], where the assumption that the operators are real plays a crucial role and our aim of this paper is to study the operators with complex coefficients. Our method may be considered as a generalization of the usual variational method replacing the Gårding inequality by the estimate (2.15), (cf. [3], [5]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 66 , May 1977 , pp. 1 - 12
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

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[8] Matsuzawa, T.: On a hypoelliptic boundary value problem, Nagoya Math. J. (to appear).Google Scholar
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