We consider shape functionals of the form Fq(Ω) = P(Ω) Tq(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 Fq(Ω) is considered on various classes of admissible domains Ω : in the class Aall of all domains, in the class Aconvex of convex domains, and in the class Athin of thin domains.
Some Inequalities Involving Perimeter and Torsional Rigidity
Buttazzo G.
Secondo
;Prinari F.Ultimo
2021
Abstract
We consider shape functionals of the form Fq(Ω) = P(Ω) Tq(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 Fq(Ω) is considered on various classes of admissible domains Ω : in the class Aall of all domains, in the class Aconvex of convex domains, and in the class Athin of thin domains.File in questo prodotto:
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