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中国科学院大学学报 ›› 2013, Vol. 30 ›› Issue (3): 293-297.DOI: 10.7523/j.issn.1002-1175.2013.03.002

• 数学 • 上一篇    下一篇

带有低阶项的非散度椭圆方程解的二阶导数的高阶可积性

白晋彦, 崔学伟   

  1. 西北工业大学应用数学系教育部空间物理和化学重点实验室, 西安 710129
  • 收稿日期:2012-01-09 修回日期:2012-05-07 发布日期:2013-05-15
  • 通讯作者: CUI Xue-Wei, E-mail:c88xw@163.com
  • 基金资助:

    Supported by National Natural Science Foundation of China(11001221), Mathematical Tianyuan Foundation of China (11126027) and Northwestern Polytechnical University Jichu Yanjiu Jijin Tansuo Xiangmu(JC201124)

Higher integrability result for solutions to nondivergence elliptic equations with low-order terms

BAI Jin-Yan, CUI Xue-Wei   

  1. Department of Applied Mathematics, Key Laboratory of Space Physics and Chemistry, Ministry of Education, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, China
  • Received:2012-01-09 Revised:2012-05-07 Published:2013-05-15

摘要:

研究如下形式的非散度椭圆方程

解的二阶导数的高阶可积性,其中系数aij(x)有界且具有小BMO范数,bi(x), c(x)Ln(Ω),Ω为Rn(n≥3)中的有界光滑域.

关键词: 非散度椭圆方程, 小BMO范数, 高阶可积性

Abstract:

We establish a higher integrability for second derivatives of solutions to the nondivergence elliptic equations of the following type ,

where the coefficients aij(x) are bounded and have small BMO-norm, and bi(x) and c(x) belong to Ln(Ω) where Ω is a bounded smooth domain in Rn(n≥3).

Key words: nondivergence elliptic equation, small BMO-norm, higher integrability

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