On Location of Maximum of Gradient of Torsion Function

• DOI: 10.1137/23m1609452
• Publication Date: 2024-07-29T08:10:58Z
• Authors: Qinfeng Li; Ruofei Yao
• Keywords: Mathematics - Analysis of PDEs; 0203 mechanical engineering; FOS: Mathematics; 02 engineering and technology; Analysis of PDEs (math.AP)

.It has been a widely-accepted belief that for planar convex domain with two coordinate axes of symmetry, the location maximal norm gradient torsion function is either linked to contact points largest inscribed circle or connected on boundary minimal curvature. However, we show this not quite true in general. Actually, derive precise formula nearly ball domains \(\mathbb{R}^n\) , which displays nonlocal nature and thus does inherently establish connection aforementioned types points. Consequently, explicit counterexamples can be straightforwardly constructed illustrate deviation from conventional understanding. We also prove rectangular domain, maximum exactly occurs at centers faces \((n - 1)\) -volume.Keywordstorsion functiondomain variationharmonic extensionMSC codes35B5074B0535B05