Semiclassical Cauchy Estimates and Applications

2013/02/21 by Long Jin, Jin, Long
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1302.5363

arxiv created 2013/02/21 · arxiv updated 2013/02/22

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.

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