On the Cheeger problem for rotationally invariant domains

被引：5

作者：

Bobkov, Vladimir ^{[1
,2
]}

Parini, Enea ^{[3
]}

机构：

[1] Univ West Bohemia, Dept Math & NTIS, Fac Appl Sci, Univ 8, Plzen 30100, Czech Republic

[2] RAS, Ufa Fed Res Ctr, Inst Math, Chernyshevsky Str 112, Ufa 450008, Russia

[3] Aix Marseille Univ, CNRS, Cent Marseille, I2M, 39 Rue Frederic Joliot Curie, F-13453 Marseille, France

来源：

MANUSCRIPTA MATHEMATICA | 2021年 / 166卷 / 3-4期

关键词：

SETS; REGULARITY; UNIQUENESS; CONSTANT;

D O I：

10.1007/s00229-020-01260-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the properties of the Cheeger sets of rotationally invariant, bounded domains Omega subset of R-n. For a rotationally invariant Cheeger set C, the free boundary partial derivative C boolean AND Omega consists of pieces of Delaunay surfaces, which are rotationally invariant surfaces of constant mean curvature. We show that if Omega is convex, then the free boundary of C consists only of pieces of spheres and nodoids. This result remains valid for nonconvex domains when the generating curve of C is closed, convex, and of class C-1,C-1. Moreover, we provide numerical evidence of the fact that, for general nonconvex domains, pieces of unduloids or cylinders can also appear in the free boundary of C.

引用

页码：503 / 522

页数：20

共 26 条

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