Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains

被引：11
|
作者：
Byun, Sun-Sig [1 ]
Wang, Lihe [2 ,3 ]
机构：
[1] Seoul Natl Univ, Dept Math, Seoul 151747, South Korea
[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
[3] Xi An Jiao Tong Univ, Coll Sci, Xian 710049, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 11期
关键词：
W-2; W-p estimates; Fourth-order parabolic equations; BMO space; Reifenberg domains; Vitali covering lemma; Fractals;
D O I：
10.1016/j.jde.2008.03.028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study optimal W-2.p-regularity for fourth-order parabolic equations with discontinuous coefficients in general domains. We obtain the global W-2.p-regulafity for each 1 < p < infinity under the assumption that the coefficients have suitably small BMO semi-norm of weak type and the boundary of the domain is delta-Reifenberg flat. The situation of our main theorem arises when the conductivity on fractals is controlled by a random variable in the time direction. (C) 2008 Elsevier Inc. All rights reserved.
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页码：3217 / 3252
页数：36
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