Semiclassical Cauchy Estimates and Applications
Analysis of PDEs
2013-02-22 v1
Abstract
In this note, we study solutions to semiclassical Schrodinger equations on a real analytic manifold with a real analytic potential and prove the semiclassical version of Cauchy estimates on derivatives. As an application, we use Donnelly and Fefferman's method to prove the upper and lower bounds for (n-1)-dimensional Hausdorff measure of the nodal sets of the solutions to semiclassical Schrodinger equations.
Cite
@article{arxiv.1302.5363,
title = {Semiclassical Cauchy Estimates and Applications},
author = {Long Jin},
journal= {arXiv preprint arXiv:1302.5363},
year = {2013}
}