PreprintCC BY 4.0arXiv
A sharp lower bound for torsional rigidity of convex domains
Abstract
For every bounded convex domain Ω⊂ℝd, d≥2, we establish the following sharp inequality for torsional rigidity T(Ω)≥(2(d+1))/d∫Ωdist(x,∂Ω)2dd x, where T(Ω)=4∫Ωudd x and −Δu=1 in Ω, u∈ H10(Ω). Equality holds for balls.
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BibTeX
@misc{perelmuter2026sharp,
title = {{A sharp lower bound for torsional rigidity of convex domains}},
author = {M. A. Perelmuter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39666},
eprint = {2610.39666},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39666},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A sharp lower bound for torsional rigidity of convex domains
AU - M. A. Perelmuter
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39666
UR - https://arxiv.org/abs/2610.39666
AB - For every bounded convex domain Ω⊂ℝ^d, d≥2, we establish the following sharp inequality for torsional rigidity T(Ω)≥(2(d+1))/d∫_Ωdist(x,∂Ω)^2dd x, where T(Ω)=4∫_Ωudd x and −Δu=1 in Ω, u∈ H^1_0(Ω). Equality holds for balls.
ER -