On a class of nonhyperbolic microdifferential equations with involutory double characteristics

The 2-Microlocal Canonical Form for a Class of Microdifferential Equations and Propagation of Singularities

“…and showed that (0. 1) is equivalent to A M~ 0 or Aw = 0 or u = 0 as a 2-microdifferential equation 0 In this paper, we generalize the result of [8] mentioned above to a class of microdifferentiai equation of which microlocal canonical form is (0.2) P 1 u= (D^D™ 2 + (lower) ) u = 0 defined in a neighborhood of (0, dz^) £;T*C n , We assume that In hyperbolic case, we study the propagation of microlocal singularities of the solutions of the equation whose model is (0, 2). Now we give the plan of this paper.…”

“…In [8], the author dealt with a class of equation whose microlocal model is (0. 1 ) P 0 u = (A A + (lower) ) u = 0 defined in a neighborhood of (0, rf^3) ^T*C n .…”

“…In [8], the author dealt with a class of equation whose microlocal model is We prove that (0. 2) is equivalent to…”

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IntroductionWe study a class of microdifferentiai equations with involutory double characteristics.In [8], the author dealt with a class of equation whose microlocal model is We prove that (0. 2) is equivalent to

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Microdifferential Equations With Isotropic Intersections

“…In this case Theorem 1 is $\mathrm{w}\mathrm{e}\mathrm{U}$ -known under some assumptions for the lower order terms (See [8,19]). [15] considered this case without such assumptions in the second microlocal category. On the other hand, in the second case our assumption Al is the usual Levi condition for Fuchsian operators, and $I_{P}(\epsilon)$ is also the usual indicial polynomial.…”