《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (6): 76-83.doi: 10.6040/j.issn.1671-9352.0.2019.871
• • 上一篇
张雅楠,杨雅琦,佟玉霞*
ZHANG Ya-nan, YANG Ya-qi, TONG Yu-xia*
摘要: 研究一类A-调和方程对应障碍问题弱解的局部梯度估计,首先获得其局部Lp估计,然后再使用新标准化方法和迭代覆盖逼近方法将其推广到Orlicz空间。
中图分类号:
[1] CHOE H J. A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems[J]. Archive for Rational Mechanics and Analysis, 1991, 114(4):383-394. [2] LIANG Shuang, ZHENG Shenzhou. Gradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities[J]. Electronic Journal of Differential Equations, 2018, 2018(58):1-15. [3] YAO Fengping. Gradient estimates for weak solutions of A-harmonic equations[J]. Journal of Inequalities and Applications, 2010(1):1-19. [4] BYUN S S, LEE M. Weighted estimates for nondivergence parabolic equations in Orlicz spaces[J]. Journal of Functional Analysis, 2015, 269(8):2530-2563. [5] BYUN S S, YAO Fengping, ZHOU Shulin. Gradient estimates in Orlicz space for nonlinear elliptic equations[J]. Journal of Functional Analysis, 2008, 255(8):1851-1873. [6] GIAQUINTA M. Multiple integrals in the calculus of variations and nonlinear elliptic systems[M]. Princeton: Princeton University Press, 1983. [7] 高红亚, 贾苗苗. 障碍问题解的局部正则性和局部有界性[J]. 数学物理学报, 2017, 37(4):706-713. GAO Hongya, JIA Miaomiao. Local regularity and local boundedness for solutions to obstacle problems[J]. Acta Mathematica Scientia, 2017, 37(4):706-713. [8] YAO Fengping, SUN Yu, ZHOU Shulin. Gradient estimates in Orlicz spaces for quasilinear elliptic equation[J]. Nonlinear Analysis, 2008, 69(8):2553-2565. [9] HEINONEN J, KILPELANEN T, MARTIO O. Nonlinear potential theory of degenerate elliptic equations[M]. New York: Clarendon Press, 1993. [10] LIEBRMAN G M. The natural generalization of the natural conditions of Ladyzhenskaya and Urall'tseva for elliptic equations[J]. Communications in Partial Differential Equations, 1991, 16(2/3):311-361. |
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[3] | 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. |
[4] | 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. |
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[6] | 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. |
[7] | 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. |
[8] | 许万银. 一类拟线性Neumann问题的多重解[J]. J4, 2009, 44(10): 39-42. |
[9] | 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 . |
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