Year: 2026
Type: preprint
Abstract: For every bounded convex domain $Ω\subset\mathbb R^d$, $d\ge2$, we establish the following sharp inequality for torsional rigidity $$T(Ω)\ge\frac{2(d+1)}{d}\int\limits_Ω\operatorname{dist}(x,\partialΩ)^2\,\mathrm{d} x,$$ where $T(Ω)=4\int\limits_Ωu\,\mathrm{d} x$ and $-Δu=1$ in $Ω$, $u\in H^1_0(Ω)$. Equality holds for balls.
Source: arXiv (Cornell University)
Author: Perelmuter, M. A.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224760603