Some inequalities involving perimeter and torsional rigidity

L. Briani, G. Buttazzo, F. Prinari

We 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…