Semialgebraic Calderon-Zygmund theorem on regularization of the distance function

被引：0

作者：

Kocel-Cynk, Beata ^{[1
]}

Pawlucki, Wieslaw ^{[2
]}

Valette, Anna ^{[3
]}

机构：

[1] Politechniki Krakowskiej, Inst Matematyki, ul Warszawska 24, PL-31155 Krakow, Poland

[2] Univ Jagiellonskiego, Inst Matematyki, ul Prof St Lojasiewicza 6, PL-30048 Krakow, Poland

[3] Univ Jagiellonskiego, Katedra Teorii Optymalizacji & Sterowan, ul Prof St Lojasiewicza 6, PL-30048 Krakow, Poland

来源：

MATHEMATISCHE ANNALEN | 2024年 / 390卷 / 02期

关键词：

EXTENSION THEOREM; VERSION;

D O I：

10.1007/s00208-023-02795-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that, for any closed semialgebraic subset W of R-n and for any positive integer p, there exists a Nash function f : R-n -> (0,infinity) which is equivalent to the distance function from W and at the same time it is Lambda(p) -regular in the sense that |D-alpha f(x)| <= Cd(x,W)(1-|alpha|), for each x is an element of R-n\W and each alpha is an element of N-n such that 1 <= |alpha| <= p, where C is a positive constant. In particular, f is Lipschitz. Some applications of this result are given.

引用

页码：1863 / 1883

页数：21