Regularity of hyperbolic magnetic Schr\"odinger equation with oscillating coefficients
Analysis of PDEs
2016-09-13 v1
Abstract
This paper mainly discuss the regularity behavior of the hyperbolic magnetic Schroedinger equation with singular coefficients near the origin. We apply the techniques from the microlocal analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the result, a delicate counterexample with periodic coefficients will be constructed to show the lower bound of loss of regularity by the application of harmonic analysis and instability arguments.
Keywords
Cite
@article{arxiv.1609.03406,
title = {Regularity of hyperbolic magnetic Schr\"odinger equation with oscillating coefficients},
author = {Xiaojun Lu and Xiaofen Lv},
journal= {arXiv preprint arXiv:1609.03406},
year = {2016}
}
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