The Minkowski Problem for Torsional Rigidity

作者：Colesanti Andrea^*; Fimiani Michele

来源：Indiana University Mathematics Journal, 2010, 59(3): 1013-1039.

DOI：10.1512/iumj.2010.59.3937

• Minkowski problem
• torsional rigidity
• convex 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 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.

• 出版日期2010