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

Hörmann, Günther; Oberguggenberger, Michael; Pilipović, Stevan

doi:10.1090/S0002-9947-05-03759-1

Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients
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by Günther Hörmann, Michael Oberguggenberger and Stevan Pilipović PDF

Trans. Amer. Math. Soc. 358 (2006), 3363-3383 Request permission

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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