From the Brunn-Minkowski inequality to a class of generalized Poincaré-type inequalities for torsional rigidity

2023/07/24 by Fang, Niufa, Hu, Jinrong, Zhao, Leina
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.12738

Abstract

In this paper, we establish a class of generalized Poincaré-type inequalities for torsional rigidity on the boundary of a convex body of class C²₊ in \rnnn by using the concavity of related Brunn-Minkowski inequality.

Related

• From the Brunn-Minkowski inequality to a class of Poincaré type inequalities
• The Minkowski problem for the torsional rigidity
• Functional inequalities derived from the Brunn-Minkowski inequalities for quermassintegrals
• The L_p-Brunn-Minkowski inequalities for variational functionals with 0≤ p<1
• The Lp Minkowski problem for q-torsional rigidity