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
[1] RUZICKA M. Electrorheological fluids: modeling and mathematical theory[J]. Lecture Notes in Mathematics, 2000, 1748(1):16-38.
[2] RAJAGOPAL K R, RUZICKA M. Mathematical modeling of electrorheological materials[J]. Continuum Mechanics and Thermodynamics, 2001, 13(1):59-78.
[3] CHEN Y M, LEVINE S, RAO M. Variable exponent, linear growth functionals in image restoration[J]. SIAM Journal on Applied Mathematics, 2006, 66(4):1383-1406.
[4] 佟玉霞, 谷建涛, 徐秀娟. 一类非齐次A-调和方程很弱解的正则性[J]. 高校应用数学学报(A辑), 2009, 24(3):319-323. TONG Yuxia, GU Jiantao, XU Xiujuan. Regularity for very weak solutions to A-harmonic equation[J]. Applied Mathematics A Journal of Chinese Universities(Ser.A), 2009, 24(3):319-323.
[5] 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. XU Xiujuan, YAN Shuo, ZHU Yeqing. Global regularity for very weak solutions to non-homogeneous A-harmonic equation[J]. Journal of Shandong University(Natural Science), 2020, 55(2):48-56.
[6] YAO Fengping. Gradient estimates for weak solutions of A-harmonic equations[J]. Journal of Inequalities and Applications, 2010, 2010(1):1-18.
[7] 张雅楠, 闫硕, 佟玉霞. 自然增长条件下的非齐次A-调和方程弱解的梯度估计[J]. 数学物理学报, 2020, 40(2):379-394. ZHANG Yanan, YAN Shou, TONG Yuxia. Gradient estimates for weak solutions to A-harmonic equation under natural growth[J]. Acta Mathematica Scientia, 2020, 40(2):379-394.
[8] 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. ZHANG Yanan, YANG Yaqi, TONG Yuxia. Gradient estimates for weak solutions to A-harmonic equation[J]. Journal of Shandong University(Natural Science), 2020, 55(6):76-83.
[9] YAO Fengping. Weighted gradient estimates for the general elliptic p(x)-Laplace equations[J]. Journal of Mathematical Analysis and Applications, 2014, 415(2):644-660.
[10] ZHENG Shenzhou, LIANG Shuang. Gradient estimate in Orlicz spaces for eliptic obstacle problems with partlally BMO non-linearities[J]. Electronic Journal of Differential Equations, 2018, 2018(58):1-15.
[11] ACERBI E, MINGIONE G. Gradient estimate for the p(x)-Laplacean system[J]. Journal Für Die Reine and Angewandte Mathematik, 2005, 584(16):117-148.
[12] ACERBI E, FUSCO N. Regularity for minmizers of nonquadratic functionals: the case 1<p<2[J]. Journal of Mathematical Analysis and Applications, 1989, 140(1):115-135.
[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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