Localisation for the torsion function and the strong Hardy inequality

Michiel van den Berg, Thomas Kappeler

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Abstract

Two-sided bounds for the efficiency of the torsion function are obtained in terms of the square of the distance to the boundary function under the hypothesis that the Dirichlet Laplacian satisfies a strong Hardy inequality. Localisation properties of the torsion function are obtained under that hypothesis. An example is analysed in detail.
Original languageEnglish
Pages (from-to)514-531
Number of pages18
JournalMathematika
Volume67
Issue number2
Early online date15 Mar 2021
DOIs
Publication statusE-pub ahead of print - 15 Mar 2021

Keywords

  • Torsion function
  • Dirichlet boundary condition
  • localisation
  • efficiency
  • Hardy inequality

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