Relaxation of convex functional:: The gap problem

被引：41
作者：
Acerbi, E
Bouchitté, G
Fonseca, I [1 ]
机构：
[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
[2] Univ Parma, Dipartimento Matemat, I-43100 Parma, Italy
[3] Univ Toulon & Var, Dept Math, F-83957 La Garde, France
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2003年 / 20卷 / 03期
基金：
美国国家科学基金会;
关键词：
convexity; Besicovich covering theorem; Radon Nikodym derivative; Lavrentiev phenomenon;
D O I：
10.1016/S0294-1449(02)00017-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown that the relaxed energy [GRAPHICS] admits the representation [GRAPHICS] where f is a convex, Caratheodory integrand satisfying a nonstandard "alpha-beta" growth hypothesis, beta is an element of [alpha, Nalpha (N - 1)). Sufficient conditions guaranteeing that mu(s)(u, (.)) = 0 are discussed. An example asserting that this representation may fail in the quasiconvex case is provided. (C) 2003 Editions scientifiques et medicales Elsevier SAS.
引用
收藏
页码：359 / 390
页数：32
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