Euclidean balls solve some isoperimetric problems with nonradial weights

被引：20

作者：

Cabre, Xavier

Ros-Oton, Xavier ^{[1
]}

Serra, Joaquim ^{[1
]}

机构：

[1] Univ Politecn Cataluna, Dept Matemat Aplicada, E-08028 Barcelona, Spain

来源：

COMPTES RENDUS MATHEMATIQUE | 2012年 / 350卷 / 21-22期

关键词：

INEQUALITIES; CONES;

D O I：

10.1016/j.crma.2012.10.031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this Note we present the solution of some isoperimetric problems in open convex cones of R-n in which perimeter and volume are measured with respect to certain nonradial weights. Surprisingly, Euclidean balls centered at the origin (intersected with the convex cone) minimize the isoperimetric quotient. Our result applies to all nonnegative homogeneous weights satisfying a concavity condition in the cone. When the weight is constant, the result was established by Lions and Pacella in 1990. (c) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：945 / 947

页数：3

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