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

共 24 条

[11] Geometrical Structure of Laplacian Eigenfunctions [J].

Grebenkov, D. S. ;

Nguyen, B. -T. .

SIAM REVIEW, 2013, 55 (04) :601-667

[12] ON TWO FUNCTIONALS INVOLVING THE MAXIMUM OF THE TORSION FUNCTION [J].

Henrot, Antoine ;

Lucardesi, Ilaria ;

Philippin, Gerard .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2018, 24 (04) :1585-1604

[13] SOME INEQUALITIES FOR THE 1ST POSITIVE ZEROS OF BESSEL-FUNCTIONS [J].

LORCH, L .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (03) :814-823

[14]

Payne L. E., 1973, Applicable Analysis, V3, P295, DOI 10.1080/00036817308839071

[15]

Simon B., 1979, FUNCTIONAL INTEGRATI

[16]

Sperb R, 1981, MAXIMUM PRINCIPLES A

[17] LOCALIZATION FOR THE TORSION FUNCTION AND THE STRONG HARDY INEQUALITY [J].

van den Berg, M. ;

Kappeler, T. .

MATHEMATIKA, 2021, 67 (02) :514-531

[18] Spectral Bounds for the Torsion Function [J].

van den Berg, M. .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2017, 88 (03) :387-400

[19] On Plya's Inequality for Torsional Rigidity and First Dirichlet Eigenvalue [J].

van den Berg, M. ;

Ferone, V. ;

Nitsch, C. ;

Trombetti, C. .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2016, 86 (04) :579-600

[20] Hardy inequality and Lp estimates for the torsion function [J].

van den Berg, M. ;

Carroll, Tom .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2009, 41 :980-986

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