On Efficiency and Localisation for the Torsion Function

被引：4

作者：

van den Berg, M. ^{[1
]}

Bucur, D. ^{[2
]}

Kappeler, T. ^{[3
]}

机构：

[1] Univ Bristol, Sch Math, Woodland Rd,Fry Bldg, Bristol BS8 1UG, Avon, England

[2] Univ Savoie Mont Blanc, UMR CNRS 5127, Lab Math, F-73376 Le Bourget Du Lac, France

[3] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

来源：

POTENTIAL ANALYSIS | 2022年 / 57卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

Torsion function; First Dirichlet eigenfunction; Schrodinger operator; Dirichlet boundary condition; Localisation; Efficiency; INEQUALITY; RIGIDITY;

D O I：

10.1007/s11118-021-09928-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the torsion function for the Dirichlet Laplacian -Delta, and for the Schrodinger operator -Delta + V on an open set Omega subset of R-m of finite Lebesgue measure 0 < vertical bar Omega vertical bar < infinity with a real-valued, non-negative, measurable potential V. We investigate the efficiency and the phenomenon of localisation for the torsion function, and their interplay with the geometry of the first Dirichlet eigenfunction.

引用

页码：571 / 600

页数：30

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