THE CONSTRAINED LEAST GRADIENT PROBLEM IN RN

被引：7

作者：

STERNBERG, P ^{[1
]}

WILLIAMS, G ^{[1
]}

ZIEMER, WP ^{[1
]}

机构：

[1] UNIV WOLLONGONG,DEPT MATH,WOLLONGONG,NSW 2500,AUSTRALIA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1993年 / 339卷 / 01期

关键词：

D O I：

10.2307/2154226

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the constrained least gradient problem inf{integral-(OMEGA) \del u\ dx:u is-an-element-of C0,1 (OMEGABAR), \delu\ less-than-or-equal-to 1a.e., u = g on partial derivative OMEGA} which arises as the relaxation of a nonconvex problem in optimal design. We establish the existence of a solution by an explicit construction in which each level set is required to solve an obstacle problem. We also establish the uniqueness of solutions and discuss their structure.

引用

页码：403 / 432

页数：30

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