In this paper we study the behavior of degenerate parabolic equations of the formv(x) ut(x,t) = Σni,j=1 Dxi (aij(x,t) Dxi u(x,t)),where the coefficients are measurable functions.
L’étude de la dynamique semi-classique d’électrons dans un cristal débouche naturellement sur le problème de l’évolution des mesures semi-classiques en présence d’un croisement de modes. Dans ce travail, nous étudions un système qui présente un tel croisement. À cet effet, nous introduisons des mesures semi-classiques à deux échelles qui décrivent comment la transformée de Wigner usuelle se concentre sur l’ensemble des trajectoires rencontrant ce croisement. Puis nous établissons des formules...
A survey of the fundamental ideas which are the base of the socalled symmetrization method; a priori estimates in partial differential equations.
This work is devoted to a systematic study of the microlocal regularity properties of pseudo-differential operators with the transmission property. We introduce a “boundary singular spectrum”, denoted for distributions , regular in the normal variable (thus, means that near the boundary), and it is shown that is a subset of if has degree and the transmission property. We finally prove that these results can bef used to examinate the (microlocal) regularity of the solutions of differential...
We obtain some microlocal estimates of the resonant states associated to a resonance of an -differential operator. More precisely, we show that the normalized resonant states are