JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 47-55.doi: 10.6040/j.issn.1671-9352.0.2020.563

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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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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

CLC Number: 

  • O175.25
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[1] ZHANG Ya-nan, YANG Ya-qi, TONG Yu-xia. Local gradient estimates for weak solutions of obstacle problems to a class of A-harmonic equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 76-83.
[2] XU Xiu-juan, YAN Shuo, ZHU Ye-qing. Global regularity for very weak solutions to non-homogeneous A-harmonic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 48-56.
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