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Propagation de la polarisation pour des problèmes aux limites convexes pour les bicaractéristiques. (Propagation of the polarization for convex boundary value problems for the bicharacteristics). (French) Zbl 0593.58037
The author considers the boundary value problem \[ D_ xu=G(x,y,D_ y)u,\quad x>0,\quad y\in R^ n,\quad \beta (y,D_ y)u=0,\quad x=0\quad y\in R^ n \] where u is vector-valued. \(D_ x-G\) is of real principal type, the principal symbol of G can be reduced to a suitable block form, and \(\beta\) satisfies the Lopatinskij-Shapiro condition. The following results are established. The polarized wavefront set propagates along Hamiltonian orbits above null bicharacteristic strips transversal to \(x=0\) (when \(x>0\), this is an earlier result of Denker). In the gliding case, the polarized wavefront set propagates along boundary Hamiltonian orbits (which lie above gliding rays). Interaction of polarization between transversal and gliding rays is also studied.
Reviewer: P.Godin

MSC:
58J32 Boundary value problems on manifolds
58J47 Propagation of singularities; initial value problems on manifolds
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