WHEN THE 3D MAGNETIC LAPLACIAN MEETS A CURVED EDGE IN THE SEMICLASSICAL LIMIT

被引：6
|
作者：
Popoff, Nicolas [1 ]
Raymond, Nicolas [1 ]
机构：
[1] Univ Rennes 1, IRMAR, UMR 6625, F-35042 Rennes, France
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 04期
关键词：
spectral theory; magnetic Schrodinger operator; semiclassical analysis; nonsmooth boundary; microlocalization; normal form; SCHRODINGER OPERATOR; NEUMANN LAPLACIAN; SPECTRAL ASYMPTOTICS; EIGENVALUE PROBLEMS; FIELD; SUPERCONDUCTIVITY; BOTTLES; DOMAINS; CORNERS; NUCLEATION;
D O I：
10.1137/130906003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the magnetic Laplacian in the case when the Neumann boundary contains an edge. We provide complete asymptotic expansions in powers of h(1/4) of the low lying eigenpairs in the semiclassical limit h -> 0. In order to get our main result we establish a general method based on a normal form procedure, microlocal arguments, the Feshbach-Grushin reduction, and the Born-Oppenheimer approximation.
引用
收藏
页码：2354 / 2395
页数：42
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