On efficiency and localisation for the torsion function

Michiel van den Berg, Dorin Bucur, Thomas Kappeler

Research output: Contribution to journalArticle (Academic Journal)peer-review


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


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


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