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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (6): 46-56.doi: 10.6040/j.issn.1671-9352.0.2022.520

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一类非一致椭圆方程障碍问题的全局BMO估计

郭艳敏(),赵崧,佟玉霞*()   

  1. 华北理工大学理学院, 河北 唐山 063210
  • 收稿日期:2022-10-07 出版日期:2023-06-20 发布日期:2023-05-23
  • 通讯作者: 佟玉霞 E-mail:guoyanmin1125@126.com;tongyuxia@126.com
  • 作者简介:郭艳敏(1997—), 女, 硕士研究生, 研究方向为偏微分方程及应用. E-mail: guoyanmin1125@126.com

Global BMO estimations for obstacle problems of a class of non-uniformly elliptic equations

Yanmin GUO(),Song ZHAO,Yuxia TONG*()   

  1. College of Science, North China University of Science and Technology, Tangshan 063210, Hebei, China
  • Received:2022-10-07 Online:2023-06-20 Published:2023-05-23
  • Contact: Yuxia TONG E-mail:guoyanmin1125@126.com;tongyuxia@126.com

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摘要：

研究一类具有渐进正则性的非一致椭圆方程弱解的障碍问题。当渐进正则问题的解的梯度接近于无穷大时, 利用正则问题的解来逼近渐近正则问题的解, 基于Young不等式及扰动讨论等方法, 得到其障碍问题弱解梯度的全局有界平均振荡(bounded mean oscillation, BMO)估计。

关键词: 非一致椭圆方程, 障碍问题, 弱解, 全局BMO估计

Abstract:

The regularity of weak solutions to the obstacle problem for non-uniformly elliptic equations is studied. When the gradient of the solution to the asymptotic regular problem is close to infinity, the solution of the regular problem is used to obtain an approximate solution to the asymptotic regular problem, and the bounded mean oscillation (BMO) estimates of the weak solutions gradient of the obstacle problem are obtained based on the Young inequality and perturbation discussion.

Key words: non-uniformly elliptic equation, obstacle problem, weak solution, global BMO estimation

中图分类号: 

  • O175.25
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