We study, for a model class of classical pseudodifferential operators with symplectic characteristics of multiplicity k, necessary and sufficient conditions for the hypoellipticity with loss of r + k/2 derivatives (r > 0).

We give sufficient conditions to generalize Hörmander's inequality to the case of operators with multiple characteristics of order higher than two

We prove that the Cauchy problem for a class of hyperbolic operators with double characteristics and whose simple null bicharacteristics have limit points on the set of double points is not well posed in the C ∞ category, even though the usual Ivrii-Petkov conditions on the lower order terms are satisfied. According to the standard linear algebra classification these operators, at a double point, have fundamental matrices exhibiting a Jordan block of size 4 and cannot be brought into a canonical form known as “Ivrii decomposition”, due to higher order non-vanishing terms in the Taylor development of the principal symbol near the given double point.

On etudie des solutions distribution pour le probleme de Cauchy pour des equations hyperboliques fuchsiennes. On considere la propagation de leurs singularites en utilisant la notion d'ensembles de front d'onde

On considere des operateurs de la forme: Au(t,x)= Σ j h A (h-j)m (t,x,Dx)(t∂/∂t) j u(t,x) ou les A (h-j)m sont operateurs differentiels lineaires d'ordre (h-j)m, (m,h∈N) a coefficients reguliers dans un cylindre ouvert (−T,T)×ΩcR n+1 et A 0 ≡1. On construit des parametrixes a droite et a gauche pour A