《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (4): 104-110.doi: 10.6040/j.issn.1671-9352.0.2022.268
• • 上一篇
赵崧,康迪,徐秀娟*
ZHAO Song, KANG Di, XU Xiu-juan*
摘要： 研究自然增长条件下非齐次A-调和方程障碍问题弱解的正则性。首先通过证明方程障碍问题弱解的Caccippoli不等式,得到其逆Hölder不等式,其次利用Gehring引理得到其局部可积性,最后利用本质零点及相关性质得到了其零点性质。
中图分类号:
| [1] XIE Suying, FANG Ainong. Global higher integrability for the gradient of very weak solutions of a class of nonlinear elliptic systems[J]. Nonlinear Analysis, 2003, 53(7/8):1127-1147. [2] ZHENG Shenzhou, ZHENG Xueliang, FENG Zhaosheng. Optimal regularity for A-harmonic type equations under the natural growth[J]. Discrete and Continuous Dynamical Systems: Series B, 2011, 16(2):669-685. [3] ZHENG Shenzhou, ZHENG Xueliang, FENG Zhaosheng. Regularity for a class of degenerate elliptic equations with discontinuous coefficients under natural growth[J]. Journal of Mathematical Analysis and Applications, 2008, 346(2):359-373. [4] BECK L. Boundary regularity for elliptic systems under a natural growth condition[J]. Annali Di Matematica Pura Ed Applicata, 2011, 190(4):553-588. [5] 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 Shuo, TONG Yuxia. Gradient estimates for weak solutions to non-homogeneous A-harmonic equations under natural growth[J]. Acta Mathematica Scientia, 2020, 40(2):379-394. [6] LI G B, MARTIO O. Local and global integrability of gradients in obstacle problems[J]. Annales Academiae Scientiarum Fennicae Mathematica, 1994, 19(1):25-34. [7] 周树清, 胡振华, 彭冬云. 一类A-调和方程的障碍问题的很弱解的全局正则性[J]. 数学物理学报(A辑), 2014, 34(1):27-38. ZHOU Shuqing, HU Zhenhua, PENG Dongyun. Global regularity for very weak solutions to obstacle problems corresponding to a class of A-harmonic equations[J]. Acta Mathematica Scientia(Ser. A), 2014, 34(1):27-38. [8] GEHRING F W. The Lp-integrability of the partial derivatives of a quasiconformal mapping[J]. Acta Mathematica, 1973, 130:265-277. [9] GIAQUINTA M. Multiple integrals in the calculus of variations and nonlinear elliptic systems(AM-105)[M]. Princeton: Princeton University Press, 2016: 119-164. [10] ADAMS R A, FOURNIER J. Sobolev spaces[M]. Boston: Academic Press, 2003: 81-134. [11] IWANIEC T, MARTIN G. Geometric function theory and nonlinear analysis[M]. Oxford: Clarendon Press, 2001: 354-369. |
| [1] | 薛婷婷,徐燕,刘晓平. 分数阶变系数边值问题非平凡弱解的存在性[J]. 《山东大学学报(理学版)》, 2021, 56(12): 45-51. |
| [2] | 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. |
| [3] | 杜广伟. 具有次临界增长的椭圆障碍问题解的正则性[J]. 山东大学学报（理学版）, 2018, 53(6): 57-63. |
| [4] | 甄苇苇,曾剑,任建龙. 基于变分理论与时间相关的抛物型反源问题[J]. 山东大学学报（理学版）, 2018, 53(10): 61-71. |
| [5] | 江静,高庆龄,张克玉. 时标上二阶Dirichlet边值问题弱解的存在性[J]. 山东大学学报（理学版）, 2016, 51(6): 99-103. |
| [6] | 李凤萍, 陈光霞. 磁微极流体方程组弱解的正则准则[J]. 山东大学学报（理学版）, 2015, 50(05): 60-67. |
| [7] | 边东芬，原保全*. 可压缩磁流体方程组整体弱解的不存在性[J]. J4, 2011, 46(4): 42-48. |
| [8] | 李娟. 一类非齐次障碍问题的很弱解的局部可积性[J]. J4, 2010, 45(8): 66-70. |
| [9] | 许万银. 一类拟线性Neumann问题的多重解[J]. J4, 2009, 44(10): 39-42. |
| [10] | 肖 华 . 多维反射倒向随机微分方程的解对参数的连续依赖性[J]. J4, 2007, 42(2): 68-71 . |
|
||
