The Minkowski problem for the torsional rigidity Andrea ColesantiMichele Fimiani 35J0552A2052A4049N99Minkowski problemtorsional rigidityconvex bodies 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. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3937 10.1512/iumj.2010.59.3937 en Indiana Univ. Math. J. 59 (2010) 1013 - 1040 state-of-the-art mathematics http://iumj.org/access/