Some inequalities involving perimeter and torsional rigidity

2020/07/06 by Luca Briani, Briani, L., Giuseppe Buttazzo +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2007.02549

openalex publication_date 2020/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider shape functionals of the form F_q(Ω)=P(Ω)T^q(Ω) on the class of open sets of prescribed Lebesgue measure. Here q>0 is fixed, P(Ω) denotes the perimeter of Ω and T(Ω) is the torsional rigidity of Ω. The minimization and maximization of F_q(Ω) is considered on various classes of admissible domains Ω: in the class A_all of all domains, in the class A_convex of convex domains, and in the class A_thin of thin domains.

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