On efficiency and localisation for the torsion function

Michiel van den Berg*, Dorin Bucur, Thomas Kappeler

*Corresponding author for this work

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

1 Citation (Scopus)
16 Downloads (Pure)

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 languageEnglish
Pages (from-to)571-600
Number of pages30
JournalPotential Analysis
Volume57
Early online date19 May 2021
DOIs
Publication statusPublished - 1 Dec 2022

Bibliographical note

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

Keywords

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

Fingerprint

Dive into the research topics of 'On efficiency and localisation for the torsion function'. Together they form a unique fingerprint.

Cite this