Gradient estimates for higher order elliptic equations on nonsmooth domains

被引：17

作者：

Byun, Sun-Sig ^{[1
]}

Ryu, Seungjin

机构：

[1] Seoul Natl Univ, Dept Math, Seoul 151747, South Korea

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 250卷 / 01期

关键词：

Higher order equation; Orlicz space; Gradient estimate; BMO space; Reifenberg domain; Reverse Holder inequality; ORLICZ SPACES; PARABOLIC EQUATIONS; REIFENBERG DOMAINS; REGULARITY THEORY; POISSON EQUATION; MEAN OSCILLATION; BMO COEFFICIENTS; DIVERGENCE FORM; WEAK SOLUTIONS; SYSTEMS;

D O I：

10.1016/j.jde.2010.10.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish optimal gradient estimates in Orlicz space for a non-homogeneous elliptic equation of higher order with discontinuous coefficients on a nonsmooth domain Our assumption is that for each point and for each sufficiently small scale the coefficients have small mean oscillation and the boundary of the domain is sufficiently close to a hyperplane As a consequence we prove the classical W(m) (p) m = 1 2 1 < p < infinity estimates for such a higher order equation Our results easily extend to higher order elliptic and parabolic systems (C) 2010 Elsevier Inc All rights reserved

引用

页码：243 / 263

页数：21

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