Reflection of $\mathrm{C}^∞$ Singularities for a Class of Operators With Multiple Characteristics

Propagation of singularities for linearised hybrid data impedance tomography

“…As a result, the principal symbol of P * 1 P 1 + P * 2 P 2 is not of principal type, and the classical propagation theory does not provide any information on the propagation of singularities. Instead we are going to use the theory for principal symbols of constant multiplicity following [8]:…”

Microlocal regularity at the boundary for pseudo-differential operators with the transmission property (I)

“…In our case, we shall mainly use the "3WF set" as introduced, for instance in Melrose-Sjostrand [12] or Chazarain [3] (the notation of whom is being used here). This set (which is defined as a subset of the cotangent bundle to the boundary), measures in some way the lack of "tangential regularity" of a distribution.…”

“…Thus, 8WF^(i<) is nothing else than the notion of singular spectrum used in Chazarain [3], Andersson-Melrose [I], SjostrandMelrose [12]. Of course, (4.4) still remains valid in this case.…”

Régularité microlocale pour des problèmes aux limites non linéaires

“…On est alors en mesure d'étudier la notion correspondant au wavefront au bord du cas linéaire non caractéristique [3], [8] : si ueîf'-00 (R^), un point (Xo,^) de R"" 1 x {0} x R' 2 " 1 n'est pas dans 3WF^ u s'il existe un opérateur pseudodifférentiel tangentiel T d'ordre 0 elliptique en (XQ , ^) tel que Tu appartienne à H^R^.). Cette propriété tout à fait attachée à la carte, devient invariante pour une fonction réelle de classe H 5 solution de l'équation non caractéristique (0.1) si s -m ~ -=p>0 et t < s + p .…”