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Note on Hypoellipticity of a First Order Linear Partial Differential Operator

Published online by Cambridge University Press:  22 January 2016

Yoshio Kato*
Affiliation:
Department of Mathematics, Aichi University of Education, Okazaki-shi, Aichi-ken (Japan)
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Let Ω be a domain in the (n + 1)-dimensional euclidian space Rn+1. A linear partial differential operator P with coefficients in C(Ω) (resp. in Cω(Ω)) will be termed hypoelliptic (resp. analytic-hypoelliptic) in Ω if a distribution u on Ω (i.e. uD′(Ω)) is an infinitely differentiable function (resp. an analytic function) in every open set of Ω where Pu is an infinitely differentiable function (resp. an analytic function).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

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