Title: The Minkowski problem for the torsional rigidity

Authors: Andrea Colesanti and Michele Fimiani

Issue: Volume 59 (2010), Issue 3, 1013-1040

Abstract: 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 $\mathbb{R}^n$. For the existence part we apply the variational method introduced by Jerison in: Adv. Math. \textbf{122} (1996), pp. 262--279. Uniqueness follows from the Brunn-Minkowski inequality for the torsional rigidity and corresponding equality conditions.