Some Inequalities Involving Perimeter and Torsional Rigidity

摘要

Omega e consider shape functionals of the form F-q(Omega) = P(Omega)T-q(Omega) on the class of open sets of prescribed Lebesgue measure. Here q > 0 is fixed, P(Omega) denotes the perimeter of Omega and T(Omega) is the torsional rigidity of Omega. The minimization and maximization of F-q(Omega) is considered on various classes of admissible domains Omega: 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.