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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Pages (from-to) | 571-600 |
Number of pages | 30 |
Journal | Potential Analysis |
Volume | 57 |
Early online date | 19 May 2021 |
DOIs | |
Publication status | Published - 1 Dec 2022 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s).
Keywords
- torsion function
- first Dirichlet eigenfunction
- Schrodinger operator
- Dirichlet boundary condition
- localisation
- efficiency