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arXiv · 0706.4315

Cutoff Resolvent Estimates and the Semilinear Schrödinger Equation

Hans Christianson
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Abstract

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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Hans Christianson. 2007-11-19. Cutoff Resolvent Estimates and the Semilinear Schrödinger Equation. https://arxiv.org/abs/0706.4315

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