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 language | English |
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Journal | Potential Analysis |
Early online date | 19 May 2021 |
DOIs | |
Publication status | E-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).
Keywords
- torsion function
- first Dirichlet eigenfunction
- Schrodinger operator
- Dirichlet boundary condition
- localisation
- efficiency