华中师范大学学报(自然科学版)
華中師範大學學報(自然科學版)
화중사범대학학보(자연과학판)
JOURNAL OF CENTRAL CHINA NORMAL UNIVERSITY
2003年
2期
138-142
,共5页
正则性%双调和方程%差分
正則性%雙調和方程%差分
정칙성%쌍조화방정%차분
regularity%biharmonic equation%difference quotients
本文考虑了下述线性双调和方程△2u-a(x)u=f(x)在Ω中, u∈H2(Ω), (*)其中Ω RN,N＞4.对于一类函数a(x),f(x),采用差分方法给出了弱解的内部正则性结果.其结论亦适合于一些非线性双调和方程.
本文攷慮瞭下述線性雙調和方程△2u-a(x)u=f(x)在Ω中, u∈H2(Ω), (*)其中Ω RN,N＞4.對于一類函數a(x),f(x),採用差分方法給齣瞭弱解的內部正則性結果.其結論亦適閤于一些非線性雙調和方程.
본문고필료하술선성쌍조화방정△2u-a(x)u=f(x)재Ω중, u∈H2(Ω), (*)기중Ω RN,N＞4.대우일류함수a(x),f(x),채용차분방법급출료약해적내부정칙성결과.기결론역괄합우일사비선성쌍조화방정.
In this paper we consider the biharmonic equations△2u-a(x)u=f(x) in Ω,u∈ H2(Ω), ( * )where Ω is a bounded domain in RN,N＞4. For a large class of functions a(x) and f(x) ,some re-sults about the interior regularity of weak solutions for ( * ) are obtained by the analysis of certaindifference quotients. Our results are also fit for some nonlinear biharmonic equations.
