BOUND ON THE NUMBER OF NEGATIVE EIGENVALUES OF TWO-DIMENSIONAL SCHRODINGER OPERATORS ON DOMAINS

被引：3

作者：

Frank, R. L. ^{[1
,2
]}

Laptev, A. ^{[3
,4
,5
]}

机构：

[1] Ludwig Maximilans Univ Munchen, Math Inst, Theresienstr 39, D-80333 Munich, Germany

[2] CALTECH, Dept Math, Pasadena, CA 91125 USA

[3] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England

[4] Inst Mittag Leffler, Auravagen 17, S-18260 Djursholm, Sweden

[5] Siberian Fed Univ, Krasnoyarsk, Russia

来源：

ST PETERSBURG MATHEMATICAL JOURNAL | 2019年 / 30卷 / 03期

基金：

美国国家科学基金会;

关键词：

Schrodinger operator; Dirichlet Laplacian; Neumann Laplacian; Trudinger inequality; DISCRETE SPECTRUM; STATES;

D O I：

10.1090/spmj/1559

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schriidinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here it is shown that in the case of Dirichlet boundary conditions the constant in this bound can be chosen independently of the domain.

引用

页码：573 / 589

页数：17

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