A new class of ``Boundary regular'' microdifferential systems (Q1305099)

The propagation up to the boundary of the analytic singularities of the solutions of microdifferential systems is investigated in this paper by a new method. First, it is to remark that the condition of transversal ellipticity [\textit{P. D'Ancona}, \textit{N. Tose} and \textit{G. Zampieri}, Commun. Partial Differ. Equ. 15, 453-460 (1990; Zbl 0712.35004)] is replaced by a unique condition of non-microcharacterisity for the conformal of the boundary. Second, one largely use the theory of the second microlocalization at the boundary [\textit{M. Uchida} and \textit{G. Zampieri}, Publ. Res. Inst. Math. Sci. 26, 205-219 (1990; Zbl 0712.35007)]. As a result the class of treatable microdifferential systems is enlarged. A nice theorem which gives a boundary version of the microlocal Holmgren's theorem, proved by \textit{J. M. Bony} [Séminaire Goulaouic-Schwartz, 1975-1976, Exp., No. 17, (1976; Zbl 0336.35003)], is obtained too. Its statement and the proof as well are quite technically to be exactly formulated.