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.
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收藏
页码：403 / 432
页数：30
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