A NEW CLASS OF “BOUNDARY REGULAR” MICRODIFFERENTIAL SYSTEMS

We give a new criterion for the propagation up to the boundary of the analytic singularities of the solutions of mi-crodifferential systems. The class of systems we are able to treat is larger than in D’Ancona-Tose-Zampieri, 1990; namely the condition of transversal ellipticity is here replaced by the non-microcharacteristicity only for the conormal to the boundary. The method also is far different. It is perhaps the most effective application of the theory of the second microlo-calization at the boundary by Uchida-Zampieri, 1990. The microlocal theory of boundary value problems origi-nated from the works by Kataoka and Schapira in the early 80’s. In this frame the propagation of the singularities is now almost completely understood. Among other contributions we quote: Schapira, 1986, Kataoka, 1980, Schapira-Zampieri, 1987. This new contribution covers one of the few problem