The Minkowski problem for the torsional rigidity

We prove the existence and uniqueness up to translations of the solution to a Minkowski type problem for the torsional rigidity in the class of open bounded convex subsets of ℝ n . For the existence part we apply the variational method introduced by Jerison in: Adv. Math. 122 (1996), pp. 262-279. Uniqueness follows from the Brunn-Minkowski inequality for the torsional rigidity and corresponding equality conditions.