Microlocal smoothing effect for the Schrödinger evolution equation in a Gevrey class. (English) Zbl 1173.35042
The author considers a time-independent Schrödinger equation with variable coefficients, and studies the propagation of the Gevrey regularity of the solution along non-trapping Hamilton vector fields. He proves that if the initial data decays (in some conical direction), then the solution becomes regular (in a corresponding microlocal direction). For this purpose he studies the propagation of the homogeneous Gevrey wave front set, which is a refinement of the usual wave front set. Such a result is already known in analytic cases, and the author extends it to Gevrey cases using almost analytic extensions of Gevrey functions.
Reviewer: Keisuke Uchikoshi (Yokosuka)
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35A27 | Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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