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

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Authors:Günther Hörmann, Michael Oberguggenberger and Stevan Pilipovic
Journal:Trans. Amer. Math. Soc. 358 (2006), 3363-3383
MSC (2000):Primary 46F30, 35D10
DOI:https://doi.org/10.1090/S0002-9947-05-03759-1
Published electronically:May 9, 2005
MathSciNet review:2218979
Full-text PDFFree Access

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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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