Dimensional lower bounds for contact surfaces of Cheeger sets

被引：3
作者：
Caroccia, M. [1 ]
Ciani, S. [2 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy
[2] Univ Firenze, DiMaI U Dini, Vle GB Morgagni 67-A, I-50134 Florence, Italy
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2022年 / 157卷
关键词：
Cheeger sets; Cheeger constant; Constant mean curvature; Removable singularities; PDEs; REMOVABLE SINGULARITIES; DIVERGENCE; THEOREM; BOUNDARIES; REGULARITY; UNIQUENESS; CONSTANT;
D O I：
10.1016/j.matpur.2021.11.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We carry out an analysis of the size of the contact surface between a Cheeger set E and its ambient space Omega subset of R-d. By providing bounds on the Hausdorff dimension of the contact surface partial derivative E boolean AND partial derivative Omega, we show a fruitful interplay between this size itself and the regularity of the boundaries. Eventually, we obtain sufficient conditions to infer that the contact surface has positive (d -1) dimensional Hausdorff measure. Finally we prove by explicit examples in two dimensions that such bounds are optimal. (C) 2021 Elsevier Masson SAS. All rights reserved.
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页码：1 / 44
页数：44
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