The Minkowski problem for the torsional rigidity
نویسندگان
چکیده
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. AMS 2000 Subject Classification: 35J05 (primary), 52A20, 52A40, 49N99.
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