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arXiv · 2005.06366

On efficiency and localisation for the torsion function

M. van den Berg·D. Bucur·T. Kappeler
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Abstract

We consider the torsion function for the Dirichlet Laplacian $-\Delta$, and for the Schr\"odinger operator $- \Delta + V$ on an open set $\Omega\subset \R^m$ of finite Lebesgue measure $0<|\Omega|<\infty$ 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.

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M. van den Berg, D. Bucur, T. Kappeler. 2020-05-13. On efficiency and localisation for the torsion function. https://arxiv.org/abs/2005.06366

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