On efficiency and localisation for the torsion function

Michiel van den Berg, Dorin Bucur, Thomas Kappeler

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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 languageEnglish
JournalPotential Analysis
Early online date19 May 2021
Publication statusE-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).


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


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