On efficiency and localisation for the torsion function

Michiel van den Berg; Dorin Bucur; Thomas Kappeler

doi:10.1007/s11118-021-09928-x

On efficiency and localisation for the torsion function

Michiel van den Berg^*, Dorin Bucur, Thomas Kappeler

^*Corresponding author for this work

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Abstract

We consider the torsion function for the Dirichlet Laplacian −∆, and for the Schr¨odinger operator −∆ + V on an open set Ω ⊂ R m of finite Lebesgue measure 0 < |Ω| < ∞ 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.

Original language	English
Pages (from-to)	571-600
Number of pages	30
Journal	Potential Analysis
Volume	57
Early online date	19 May 2021
DOIs	https://doi.org/10.1007/s11118-021-09928-x
Publication status	Published - 1 Dec 2022

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Publisher Copyright:
© 2021, The Author(s).

Keywords

torsion function
first Dirichlet eigenfunction
Schrodinger operator
Dirichlet boundary condition
localisation
efficiency

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AU - van den Berg, Michiel

AU - Bucur, Dorin

AU - Kappeler, Thomas

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N2 - We consider the torsion function for the Dirichlet Laplacian −∆, and for the Schr¨odinger operator −∆ + V on an open set Ω ⊂ R m of finite Lebesgue measure 0 < |Ω| < ∞ 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.

AB - We consider the torsion function for the Dirichlet Laplacian −∆, and for the Schr¨odinger operator −∆ + V on an open set Ω ⊂ R m of finite Lebesgue measure 0 < |Ω| < ∞ 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.

KW - torsion function

KW - first Dirichlet eigenfunction

KW - Schrodinger operator

KW - Dirichlet boundary condition

KW - localisation

KW - efficiency

U2 - 10.1007/s11118-021-09928-x

DO - 10.1007/s11118-021-09928-x

M3 - Article (Academic Journal)

SN - 0926-2601

VL - 57

SP - 571

EP - 600

JO - Potential Analysis

JF - Potential Analysis

ER -

On efficiency and localisation for the torsion function

Abstract

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Keywords

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