The Minkowski Problem for Torsional Rigidity

被引：48

作者：

Colesanti, Andrea ^{[1
]}

Fimiani, Michele ^{[1
]}

机构：

[1] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2010年 / 59卷 / 03期

关键词：

Minkowski problem; torsional rigidity; convex bodies; CONCAVITY; CAPACITY;

D O I：

10.1512/iumj.2010.59.3937

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1013 / 1039

页数：27

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