The Minkowski problem for the torsional rigidity

2008/09/26 by Colesanti, A., Fimiani, M. · 1 citation
#35J05 #49N99. #52A20 #52A40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.0809.4580

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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