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

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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
Journal	Potential Analysis
Early online date	19 May 2021
DOIs	https://doi.org/10.1007/s11118-021-09928-x
Publication status	E-pub ahead of print - 19 May 2021

Bibliographical note

Funding Information:
MvdB and TK acknowledge support by the Leverhulme Trust through Emeritus Fellowship EM-2018-011-9, and the Swiss National Science Foundation respectively. DB was supported by the LabEx PERSYVAL-Lab GeoSpec (ANR-11-LABX-0025-01) and ANR SHAPO (ANR-18-CE40-0013).

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

Keywords

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

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title = "On efficiency and localisation for the torsion function",

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.",

keywords = "torsion function, first Dirichlet eigenfunction, Schrodinger operator, Dirichlet boundary condition, localisation, efficiency",

author = "{van den Berg}, Michiel and Dorin Bucur and Thomas Kappeler",

note = "Funding Information: MvdB and TK acknowledge support by the Leverhulme Trust through Emeritus Fellowship EM-2018-011-9, and the Swiss National Science Foundation respectively. DB was supported by the LabEx PERSYVAL-Lab GeoSpec (ANR-11-LABX-0025-01) and ANR SHAPO (ANR-18-CE40-0013). Publisher Copyright: {\textcopyright} 2021, The Author(s).",

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AU - Bucur, Dorin

AU - Kappeler, Thomas

N1 - Funding Information: MvdB and TK acknowledge support by the Leverhulme Trust through Emeritus Fellowship EM-2018-011-9, and the Swiss National Science Foundation respectively. DB was supported by the LabEx PERSYVAL-Lab GeoSpec (ANR-11-LABX-0025-01) and ANR SHAPO (ANR-18-CE40-0013). Publisher Copyright: © 2021, The Author(s).

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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)

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

ER -

On efficiency and localisation for the torsion function

Abstract

Bibliographical note

Keywords

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