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On Efficiency and Localisation for the Torsion Function
Potential Analysis ( IF 1.0 ) Pub Date : 2021-05-19 , DOI: 10.1007/s11118-021-09928-x M. van den Berg , D. Bucur , T. Kappeler
中文翻译:
扭转函数的效率与局部化
更新日期:2021-05-19
Potential Analysis ( IF 1.0 ) Pub Date : 2021-05-19 , DOI: 10.1007/s11118-021-09928-x M. van den Berg , D. Bucur , T. Kappeler
We consider the torsion function for the Dirichlet Laplacian −Δ, and for the Schrödinger operator −Δ + V on an open set \({\Omega }\subset \mathbb {R}^{m}\) 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.
中文翻译:
扭转函数的效率与局部化
我们考虑狄利克雷拉普拉斯-Δ扭转功能,并为操作者薛定谔-Δ+ V上的开集\({\欧米茄} \子集\ mathbb {R} ^ {米} \)有限Lebesgue测度的\( 0 <| {\欧米茄} | <\ infty \)与实值的非负的,可测量的电势V。我们研究了扭转函数的效率和局部化现象,以及它们与第一个Dirichlet本征函数的几何形状的相互影响。