ON THE SINGULARITIES OF CONVEX-FUNCTIONS

被引：77

作者：

ALBERTI, G ^{[1
]}

AMBROSIO, L ^{[1
]}

CANNARSA, P ^{[1
]}

机构：

[1] UNIV ROMA TOR VERGATA,DIPARTIMENTO MATEMAT 2,I-00173 ROME,ITALY

来源：

MANUSCRIPTA MATHEMATICA | 1992年 / 76卷 / 3-4期

关键词：

D O I：

10.1007/BF02567770

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a semi-convex function u : OMEGA subset-of R(n) --> R and an integer k is-an-element-of [0, n], we show that the set SIGMA(k) defined by SIGMA(k) = {x is-an-element-of OMEGA : dim(partial derivative u(x)) greater-than-or-equal-to k} is countably H(n-k)-rectifiable, i.e., it is contained (up to a H(n-k)-negligible set) in a countable union of C1 hypersurfaces of dimension (n - k). Moreover, we show that [GRAPHICS](~)for any open set OMEGA' subset-of subset-of OMEGA.

引用

页码：421 / 435

页数：15

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[2]

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