A new class of "boundary regular" microdifferential systems

We give a new criterion for the propagation up to the boundary of the analy tic singularities of the solutions of microdifferential systems. The class of systems we are able to treat is larger than in D'Ancona-Tose-Zampieri, 1 990; namely the condition of transversal ellipticity is here replaced by th e non-microcharacteristicity only for the conormal to the boundary. The met hod also is far different. It is perhaps the most effective application of the theory of the second microlocalization at the boundary by Uchida-Zampie ri, 1990. The microlocal theory of boundary value problems originated 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 contrib utions we quote: Schapira, 1986, Kataoka, 1980, Schapira-Zampieri, 1987. Th is new contribution covers one of the few problems not yet explained at lea st in the case of transversal bicharacteristics.