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山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (6): 57-63.doi: 10.6040/j.issn.1671-9352.0.2018.003

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具有次临界增长的椭圆障碍问题解的正则性

杜广伟   

  1. 西北工业大学数学系, 陕西 西安710129
  • 收稿日期:2018-01-08 出版日期:2018-06-20 发布日期:2018-06-13
  • 作者简介:杜广伟(1987— ), 男, 博士研究生, 研究方向为偏微分方程理论及其应用. E-mail: guangwei87@mail.nwpu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11771354);陕西省自然科学基础研究计划资助项目(2017JM5140)

Regularity for solutions of elliptic obstacle problems with subcritical growth

  1. Department of Mathematics, Northwestern Polytechnical University, Xian 710129, Shaanxi, China
  • Received:2018-01-08 Online:2018-06-20 Published:2018-06-13

摘要: 利用一个改进的p-调和逼近引理,首先证明了具有次临界增长的p-Laplace型拟线性椭圆障碍问题解的梯度的Morrey正则性。进一步地,利用Hölder连续函数的积分刻划引理得到了解的Hölder连续性。利用该方法避免了证明梯度的反向不等式,从而简化了证明。

关键词: 次临界增长, Morrey正则性, 椭圆障碍问题, lder连续性,

Abstract: Based on a modification of p-harmonic approximation argument, the gradients of solutions to the quasilinear elliptic p-Laplace type obstacle problems with subcritical growth enjoy the Morrey regularity are proved. Then the Hölder continuity of solutions is obtained by using the integral characterization of Hölder continuous functions. Making use of this method, one can simplify the proof avoiding the proof of a suitable reverse Hölder inequality for the gradient.

Key words: elliptic obstacle problems, lder continuity, Hö, subcritical growth, Morrey regularity

中图分类号: 

  • O175.2
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