We study microlocal boundary value problems for a class of microdifferential equations. In particular, we are interested in a class of non-microcharacteristic systems and give a result on partially holimorphic extensibility of boundary-mi-crofunction solutions. This implies at once our main theorem on propagation of singularities up to the boundary. Our result contains several examples which can not be treated by the preceding results [S] and [S-Z]. There are many results about propagation of singularities for classes of non-microcharacteristic microdifferential operators. For the interior problem, we should first mention the paper by Bony-Schapira [B-S] on propagation along leaves of regular involutive submanifolds. This result was generalized by several authors: Hanges-Sjõstrand [H-Sj], Kashiwara-Schapira [K-S 1; §9], Grigis-Schapira-Sjõstrand [G-S-Sj] and Sjõstrand [Sj; ch.15]. For propagation at the boundary, we refer to Schapira [S] and its generalization Schapira-Zampieri [S-Z].
ASJC Scopus subject areas
- Applied Mathematics