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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (2): 48-56.doi: 10.6040/j.issn.1671-9352.0.2019.408

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一类非齐次A-调和方程很弱解的全局正则性

徐秀娟,闫硕,朱叶青   

  1. 华北理工大学理学院, 河北 唐山 063210
  • 发布日期:2020-02-14
  • 作者简介:徐秀娟(1965— ), 女, 教授, 硕士生导师, 研究方向为偏微分方程及应用. E-mail:xxjluck@126.com

Global regularity for very weak solutions to non-homogeneous A-harmonic equation

XU Xiu-juan, YAN Shuo, ZHU Ye-qing   

  1. College of Science, North China University of Science and Technology, Tangshan 063210, Hebei, China
  • Published:2020-02-14

摘要: 研究形如div A(x,∇u)=f(x)的非齐次A-调和方程的边值问题,在控制增长条件、强制性条件以及非齐次项的适当可积性假设条件下,利用Hodge分解定理和Sobolev空间分析方法,得到了很弱解的全局正则性,推广了已知的结果。

关键词: 非齐次A-调和方程, Hodge分解, 全局正则性

Abstract: This paper deals with boundary value problem for non-homogeneous A-harmonic equation div(A(x,∇u))=f(x). A global regularity result is derived for very weak solutions under some controllable and coercivity conditions and some proper integrable assumptions on the nonlinear term, by using the Hodge decomposition theorem and the methods in Sobolev spaces. The results generalize the corresponding results in related literatures.

Key words: A-harmonic equation, Hodge decomposition theorem, global regularity

中图分类号: 

  • O175.25
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