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Hypoelliptic differential operators with generalized constant coefficients

Published online by Cambridge University Press:  20 January 2009

M. Nedeljkov  and
S. Pilipović
M. Nedeljkov
Affiliation:
University of Novi Sad, Faculty of Science, Institute for Mathematics, TRG D. Obradovića 4, Novi Sad, Yugoslavia
S. Pilipović
Affiliation:
University of Novi Sad, Faculty of Science, Institute for Mathematics, TRG D. Obradovića 4, Novi Sad, Yugoslavia
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Abstract

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The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε.

There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 1 , February 1998 , pp. 47 - 60
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

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