数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 706-713.

• 论文 • 上一篇    下一篇

障碍问题解的局部正则性和局部有界性

高红亚, 贾苗苗   

  1. 河北大学数学与信息科学学院 河北 保定 071002
  • 收稿日期:2016-11-27 修回日期:2017-03-21 出版日期:2017-08-26 发布日期:2017-08-26
  • 作者简介:高红亚,E-mail:ghy@hbu.cn;贾苗苗,E-mail:303286142@qq.com
  • 基金资助:

    国家自然科学基金(10371050)和河北省自然科学基金(A2015201149)

Local Regularity and Local Boundedness for Solutions to Obstacle Problems

Gao Hongya, Jia Miaomiao   

  1. College of Mathematics and Information Science, Hebei University, Hebei Baoding 071002
  • Received:2016-11-27 Revised:2017-03-21 Online:2017-08-26 Published:2017-08-26
  • Supported by:

    Supported by the NSFC (10371050) and the Natural Science Foundation of Hebei Province (A2015201149)

摘要:

该文在算子Axξ):Ω×Rn → Rn的强制性条件和控制增长条件下,考虑A-调和方程
divAx,▽ux))=0
Kψ,θ-障碍问题的解.A的原型是
Axξ)=(μ2+|ξ|2p-2/2ξμ≥0.
得到了局部正则性和局部有界性结果.

关键词: 局部正则性, 局部有界性, 障碍问题, A-调和方程

Abstract:

This paper deals with solutions to Kψ,θ-obstacle problems of the A-harmonic equation
divA (x,▽u (x))=0
under some coercivity and growth conditions on A(x,ξ):Ω×Rn → Rn whose prototype is
A (x,ξ)=(μ2+|ξ|2)p-2/2ξ,μ ≥ 0.
Local regularity and local boundedness results are obtained.

Key words: Local regularity, Local boundedness, Obstacle problem, A-Harmonic equation

中图分类号: 

  • O175.23