Properties and Applications of the Distance Functions on Open Sets of the Euclidean Space

被引：2
|
作者：
Avkhadiev, F. G. [1 ]
机构：
[1] Kazan Fed Univ, 18 Kremlyovskaya Str, Kazan 420008, Russia
来源：
RUSSIAN MATHEMATICS | 2020年 / 64卷 / 04期
基金：
俄罗斯科学基金会;
关键词：
distance function; Rademacher theorem; Motzkin theorem; approximation of open set; convex domain; Hardy type inequality; HARDY-TYPE INEQUALITIES; INTEGRAL-INEQUALITIES; DOMAINS; CONSTANTS;
D O I：
10.3103/S1066369X20040088
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For an open subset of the Euclidean space of dimension n we consider interior and exterior approximations by sequences of open sets. We prove convergence everywhere of the corresponding sequences of distance functions from boundary as well as convergence almost everywhere for their gradients. As applications we obtain several new Hardy-type inequalities that contain the scalar product of gradients of test functions and the gradient of the distance function from the boundary of an open subset of the Euclidean space.
引用
收藏
页码：75 / 79
页数：5
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