Extensions and traces of BV functions in rough domains and generalized Cheeger sets

被引：2
|
作者：
Gui, Changfeng [1 ,2 ]
Hu, Yeyao [2 ]
Li, Qinfeng [3 ]
机构：
[1] Univ Texas San Antonio, San Antonio, TX 78249 USA
[2] Cent South Univ, Sch Math & Stat, HNP LAMA, Changsha 410083, Hunan, Peoples R China
[3] Hunan Univ, Changsha, Hunan, Peoples R China
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 02期
关键词：
28A75; 46E35; 49Q15; 49Q20; DIVERGENCE-MEASURE FIELDS; GAUSS-GREEN FORMULAS; FINITE PERIMETER; THEOREM; APPROXIMATION; EQUATIONS; VECTOR;
D O I：
10.1007/s00526-022-02377-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Via the method of interior approximation, we prove trace and extension results for BV functions defined on a bounded domain omega C R-n such that omega satisfies Hn-1(& part;omega\omega(0)) < infinity , (0,1) where H(n-1 )is the (n - 1) dimensional Hausdorff measure and omega(0) is the measure-theoretic exterior of omega. Stronger results are obtained on a subclass of such domains, which are outward minimizing domains. We also obtain new weak regularity results for generalized Cheeger sets as byproducts.
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页数：19
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