中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (2): 66-68.

• 论文 • 上一篇    下一篇

当源项为 L1 时  p-Laplace 方程有界弱解的存在性

李仲庆   

  1. 吉林师范大学数学学院,吉林 四平 136000
  • 收稿日期:2017-09-06 出版日期:2018-03-25 发布日期:2018-03-25
  • 通讯作者: 李仲庆 (1984年生),男; 研究方向: 偏微分方程;E-mail: zqli_jlu@163com

Existence of bounded weak solutions to a p -Laplace equation with source term in L1

LI Zhongqing   

  1. College of Mathematics, Jilin Normal University, Siping 136000, China
  • Received:2017-09-06 Online:2018-03-25 Published:2018-03-25

摘要:

研究一个 p-Laplace方程弱解存在性问题, 方程主要的特征是源项f仅仅位于L1中。借助于方程低阶项系数与右端源项的正则化效应, 证明了弱解的先验L估计。利用一致L界, 最终得到了弱解的存在性。

关键词: p -Laplace方程, L1数据, 有界弱解

Abstract:

The existence of solutions to a  p-Laplace equation is studied. The source term f only lies in L1, which is the main feature of the problem. With the help of the regularizing effect between the coefficient of the lower order term and the source term, a priori Lregularity for its weak solutions is proved. B-y the uniform Lbound, the existence of weak solutions is obtained.

Key words: p-Laplace equations, L1 datum, bounded weak solutions

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