Bounds for the singular set of solutions to non linear elliptic systems

被引：54
|
作者：
Mingione, G
机构：
[1] Univ Parma, Dipartimento Matemat, I-43100 Parma, Italy
[2] Univ Bonn, Inst Angew Math SFB 611, D-5300 Bonn, Germany
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2003年 / 18卷 / 04期
关键词：
D O I：
10.1007/s00526-003-0209-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give new estimates for the Hausdorff dimension of the singular set of solutions to elliptic systems - div a(x,u,Du) = b(x,u,Du). If the vector fields a and b are Holder continuous with respect to the variables (x,u) with exponent alpha, then, under suitable assumptions, the Hausdorff dimension of the singular set of any weak solution is at most n-2alpha. We consider natural growth assumptions on a(x,u,Du) with respect to u and critical ones on the right hand side b(x,u,Du), with respect to Du.
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页码：373 / 400
页数：28
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