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Transactions of the American Mathematical Society

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Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients

Authors: Günther Hörmann, Michael Oberguggenberger and Stevan Pilipovic
Journal: Trans. Amer. Math. Soc. 358 (2006), 3363-3383
MSC (2000): Primary 46F30, 35D10
Published electronically: May 9, 2005
MathSciNet review: 2218979
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Abstract: We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth hypoelliptic symbols. Methodological novelties and technical refinements appear embedded into classical strategies of proof in order to cope with most delicate interferences by non-smooth lower order terms. We include simplified conditions which are applicable in special cases of interest.

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Additional Information

Günther Hörmann
Affiliation: Institut für Mathematik, Universität Wien, A-1010 Vienna, Austria

Michael Oberguggenberger
Affiliation: Institut für Technische Mathematik, Geometrie und Bauinformatik, Universität Innsbruck, Technikerstrasse 13, A-6020 Innsbruck, Austria

Stevan Pilipovic
Affiliation: Institute of Mathematics and Informatics, Faculty of Science and Mathematics, University of Novi Sad, 21000 Novi Sad, Serbia

Keywords: Partial differential operators with non-smooth coefficients, generalized (micro-) hypoellipticity, microlocal regularity, algebras of generalized functions
Received by editor(s): March 24, 2003
Received by editor(s) in revised form: May 4, 2004
Published electronically: May 9, 2005
Additional Notes: The first author was supported by FWF grant P14576-MAT
The third author was supported by the MNTR of Serbia, Project 1835
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.