Year: 2026
Type: article
Abstract: Let $$(0,L)\times E_a\subset \mathbb {R}^{d+1}$$ ( 0 , L ) × E a ⊂ R d + 1 denote the cylinder of length L , and base $$E_a\subset \mathbb {R}^{d},$$ E a ⊂ R d , where $$E_a$$ E a is an open ellipsoid with semi-axes $$a=(a_1,...,a_d)$$ a = ( a 1 , . . . , a d ) . Let $$w_{(0,L)\times E_a}$$ w ( 0 , L ) × E a denote its torsion function. Heat equation tools are used to show that (i) if $$E_a$$ E a has small eccentricity and L is sufficiently large, then the maxima of $$|\nabla w_{(0,L)\times E_a}|$$ | ∇ w ( 0 , L ) × E a | are located at the centres (0, 0) and ( L , 0) respectively, (ii) if $$E_a$$ E a has large eccentricity and L is sufficiently large, then the maxima are located on the lateral side of the cylinder.
Source: Journal of Geometric Analysis
Author: M. van den Berg
Institution: University of Bristol
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7171104740