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On some degenerate parabolic equations II

Published online by Cambridge University Press:  22 January 2016

Tadato Matsuzawa
Tadato Matsuzawa*
Affiliation:
Department of Mathematics, Nagoya University
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In the article I: [8], we have proved the hypoellipticity of a degenerate parabolic equation of the form:

where the coefficients a(x, t), b(x,t) and c(x, t) are complex valued smooth functions. The fundamental assumption on the coefficients is that Re a(x, t) satisfies the condition of Nirenberg and Treves ([8], (1.5)). To prove the hypoellipticity we have constructed recurcively the parametrices as pseudodifferential operators with parameter. This method may be viewed as an improvement of that of [9] and [7]. We have analyzed the properties of these parametrices by estimating the symbols with parameter associated with the given operator. We shall summerize these results in §3.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 52 , December 1973 , pp. 61 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

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