摘要
考虑如下的多重调和方程(-△)ku=f(x),x∈Ω,u∈Hk0(Ω)的弱解的内部正则性.其中Ω是RN中的有界光滑区域,k是正整数,H0k(Ω)是标准的Sobolev空间.对于一类函数f(x),利用差分方法得到了上述方程弱解的内部正则性,其结果也适用于一些非线性的多重调和方程.
This paper considers the interior regularity of weak solutions for polyharmonic equations {（-△）^ku=f（x）,x∈Ω,u∈H0^k（Ω） where Ω∈R^N is a bounded open domain, k is a positive integer, H0^k（Ω） is a standard Sobolev space. For a large class of functions f（x）, some results about the interior regularity of weak solutions for above equations are obtained by the analysis of certain difference quotients. Our results are also fit for some nonlinear polyharmonic equations.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
2006年第2期151-153,157,共4页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金资助项目(10471052)
关键词
内部正则性
多重调和方程
差分
interior regularity
polyharmonic equations
difference quotients
