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.
|Early online date||19 May 2021|
|Publication status||E-pub ahead of print - 19 May 2021|
Bibliographical noteFunding 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).
© 2021, The Author(s).
- torsion function
- first Dirichlet eigenfunction
- Schrodinger operator
- Dirichlet boundary condition