We give a new criterion for
the propagation up to the boundary of the analytic singularities of the solutions of
microdifferential 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 microlocalization at the boundary by Uchida-Zampieri,
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 contributions we
quote: Schapira, 1986, Kataoka, 1980, Schapira-Zampieri, 1987. This new
contribution covers one of the few problems not yet explained at least in the case of
transversal bicharacteristics.
