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The Minkowski problem for the torsional rigidity

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arxiv 0809.4580 v1 pith:Z4SSFLI5 submitted 2008-09-26 math.AP math.MG

A. Colesanti , M. Fimiani This is my paper · ORCID
classification math.APmath.MG
keywords rigiditytorsionalexistenceminkowskiproblemuniquenessvariationalanalogous
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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 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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