Abstract
1.1. In the study of the regularity of generalized solutions of various problems for partial differential equations the notion of the hypoellipticity of linear partial differential operators has a central role. Originally the hypoelliptic operators were introduced by L. Hormander in 1955, and for the results of the development one can today consult his monograph [13], especially chapters LL and 1.3. A linear differential operator P(.,D) defined in some open set O in R through
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