Cutoff Resolvent Estimates and the Semilinear Schr\"odinger Equation
Analysis of PDEs
2007-11-19 v2
Abstract
This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schr\"odinger 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 Schr\"odinger equation.
Keywords
Cite
@article{arxiv.0706.4315,
title = {Cutoff Resolvent Estimates and the Semilinear Schr\"odinger Equation},
author = {Hans Christianson},
journal= {arXiv preprint arXiv:0706.4315},
year = {2007}
}
Comments
8 pages, 1 figure