On the relations between principal eigenvalue and torsional rigidity

Michiel van den Berg, Giuseppe Buttazzo, Aldo Pratelli

We consider the problem of minimising or maximising the quantity $\lambda (Ø)T^q(Ø)$ on the class of open sets of prescribed Lebesgue measure. Here $q>0$ is fixed, $\lambda (Ø)$ denotes the firs…