Propagation at the Boundary and Reflection of Analytic Singularities of Solutions of Linear Partial Differential Equations I.

Abstract

We study, microlocally, the non elliptic boundary value problems, with the help of the sheaf ${\mathcal{C}}_{N/X}$ of Kashiwara and Kawaï. A hypothesis of “N-regularity” verified by several classes of preudo-differential operators allows us to obtain a theorem of reflection of analytic singularities analogous to that of Lax and Nirenberg.