Kato smoothing effect for Schrödinger operator. (English) Zbl 1273.35233
Cicognani, Massimo (ed.) et al., Studies in phase space analysis with applications to PDEs. In part selected papers based on the presentations at a meeting, Bertinoro, Italy, September 2011. New York, NY: Birkhäuser/Springer (ISBN 978-1-4614-6347-4/hbk; 978-1-4614-6348-1/ebook). Progress in Nonlinear Differential Equations and Their Applications 84, 355-369 (2013).
Summary: In this paper we give a survey of results on smoothing effect for Schrödinger operators. Several phenomena can be called smoothing effect. Here we limit us on the Kato or one half smoothing effect. We shall give the new and old results in different contexts, global in time and local in time in all spaces, in exterior domain. In this last case we shall give the recent result where the geometrical control condition is not satisfied and replaced by a damping condition. This kind of assumption originates in the control theory. We shall give also some references on the other smoothing effect, Strichartz estimate and related problem for wave equation, and KdV equation without exhaustiveness.
For the entire collection see [Zbl 1263.35003].
For the entire collection see [Zbl 1263.35003].
MSC:
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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