Ramification des solutions du problème de Cauchy Fuchsien au voisinage de l'hypersurface initiale
Résumé
The purpose of this paper is the decision of the domain of ramification near the initial surface t = 0 of solutions of the Cauchy problem for a linear differential operator of Fuchs type according to Baouendi-Goulaouic. Our main result in theorem 1.1 is as follows : if, for a certain continuous function f, the datas are ramified in an open set of the form {(t,x) ∈ C×Ω; |t| < f(x)}, then the solution is ramified in an open set of the form {(t,x) ∈ C×Ω′ ; |t| < cf(x)^m}. The proof is reduced to a fuchsian equation (with an additional variable z) that is solved by the fixed-point theorem in a Banach space.