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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 47-55.doi: 10.6040/j.issn.1671-9352.0.2020.563

• • 上一篇    

非标准增长条件下A-调和方程弱解的梯度估计

周艳霞,王薪茹,徐秀娟*   

  1. 华北理工大学理学院, 河北 唐山 063210
  • 发布日期:2021-06-03
  • 作者简介:周艳霞(1996— ),女,硕士研究生,研究方向为偏微分方程及应用. E-mail:1209196943@qq.com*通信作者简介: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
  • 基金资助:
    河北省自然科学基金资助项目(A2019209005)

Gradient estimates for weak solutions of A-harmonic equation under nonstandard growth

ZHOU Yan-xia, WANG Xin-ru, XU Xiu-juan*   

  1. College of Science, North China University of Science and Technology, Tangshan 063210, Hebei, China
  • Published:2021-06-03

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摘要： 通过建立SymbolQC@u的逆Hölder不等式,采用极大函数方法,得到了形如div A(x,SymbolQC@u)=B(x,SymbolQC@u)的非齐次A-调和方程弱解的梯度估计。

关键词: 非齐次A-调和方程, 极大函数, 梯度估计

Abstract: By establishing the reverse Hölder inequality of SymbolQC@u and using the method of maximal function, the gradient estimation of the weak solution for the non-homogeneous A-harmonic equation div A(x,SymbolQC@u)=B(x,SymbolQC@u) is obtained.

Key words: A-harmonic equation, maximal function, gradient estimate

中图分类号: 

  • O175.25
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[1] 张雅楠,杨雅琦,佟玉霞. 一类A-调和方程障碍问题弱解的局部梯度估计[J]. 《山东大学学报(理学版)》, 2020, 55(6): 76-83.
[2] 徐秀娟,闫硕,朱叶青. 一类非齐次A-调和方程很弱解的全局正则性[J]. 《山东大学学报(理学版)》, 2020, 55(2): 48-56.
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