On efficiency and localisation for the torsion function

M. van den Berg; D. Bucur; T. Kappeler

On efficiency and localisation for the torsion function

Analysis of PDEs 2023-06-22 v5 Spectral Theory

Authors: M. van den Berg , D. Bucur , T. Kappeler

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.

Keywords

laplacian eigenfunctions wavelet and multifractal analysis function spaces and inequalities

Cite

@article{arxiv.2005.06366,
  title  = {On efficiency and localisation for the torsion function},
  author = {M. van den Berg and D. Bucur and T. Kappeler},
  journal= {arXiv preprint arXiv:2005.06366},
  year   = {2023}
}

Comments

33 pages. The published version in Potential Analysis (2022) 57, 571--600 has some typos: Theorem 3(i): the first exponent should read $(m-2)/m$; Example 2 Line 2: .... $B(p_{n+1};cn^{-\beta})$.....; Formula (109): $\kappa^{-1}$ missing after the second inequality

On efficiency and localisation for the torsion function

Abstract

Keywords

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