Cutoff Resolvent Estimates and the Semilinear Schrödinger Equation

@inproceedings{CHRISTIANSON2008CutoffRE,
  title={Cutoff Resolvent Estimates and the Semilinear Schr{\"o}dinger Equation},
  author={HANS CHRISTIANSON},
  year={2008}
}
  • HANS CHRISTIANSON
  • Published 2008
This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schrödinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply well-known techniques to obtain well-posedness results for the semi-linear Schrödinger equation. 
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