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 in: Adv. Math. 122 (1996), 262-276. Uniquess follows from the equality conditions in the Brunn-Monkowski inequality for the torsional rigidity.
The Minkowski problem for torsional rigidity / A. Colesanti; M. Fimiani. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 59:(2010), pp. 1013-1039. [10.1512/iumj.2010.59.3937]
The Minkowski problem for torsional rigidity
COLESANTI, ANDREA;
2010
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 the n-dimensional Euclidean space. For the existence part we apply the variational method introduced by Jerison in: Adv. Math. 122 (1996), 262-276. Uniquess follows from the equality conditions in the Brunn-Monkowski inequality for the torsional rigidity.
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