The Minkowski problem for the torsional rigidity

Details The Minkowski problem for the torsional rigidity The Minkowski problem for the torsional rigidity

2008-09-26

arxiv.org/abs/0809.4580v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

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 the $n$-dimensional Euclidean space. For the existence part we apply the variational method introduced by Jerison for analogous problems concerning other variational functionals. Uniqueness follows from the Brunn--Minkowski inequality for the torsional rigidity and corresponding equality conditions.

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