GLOBAL INTEGRABILITY FOR SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF ANISOTROPIC FUNCTIONALS

被引：0
|
作者：
Gao Hongya [1 ]
Liang Shuang [1 ]
Cui Yi [1 ]
机构：
[1] Hebei Univ, Coll Math & Informat Sci, Baoding 071002, Peoples R China
来源：
GLASNIK MATEMATICKI | 2016年 / 51卷 / 01期
关键词：
Global integrability; boundary value problem; anisotropic functional; obstacle problem; OBSTACLE PROBLEMS; MINIMIZERS; REGULARITY;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with solutions to boundary value problems of anisotropic integral functionals I(u) = integral(Omega) f(x, Du(x))dx with the energy f (x, z) has growth p(i) with respect to z(i), like in integral(Omega) ((1+Sigma(n)(j=1)vertical bar D(j)u vertical bar p(j))(P1-2/p1)vertical bar D(1)u vertical bar(2)+...+(1+Sigma(n)(j=1)vertical bar D(j)u vertical bar p(j))(Pn-2/pn)vertical bar D(n)u vertical bar(2))dx We show that higher integrability of the boundary datum u(*) forces minimizers u to be more integrable. A similar result is obtained for obstacle problems.
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页码：223 / 236
页数：14
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