华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (4): 52-61.doi: 10.3969/j.issn.1000-5641.2019.04.006

• 数学 • 上一篇    下一篇

一类具退化强制的椭圆方程熵解的存在性

代丽丽   

  1. 通化师范学院 数学学院, 吉林 通化 134002
  • 收稿日期:2018-08-01 出版日期:2019-07-25 发布日期:2019-07-18
  • 作者简介:代丽丽,女,博士,副教授,研究方向偏微分方程及其应用.E-mail:drx820115@126.com.
  • 基金资助:
    吉林省科技厅青年科研基金（20160520103JH）

Existence of entropy solutions for an elliptic equation with degenerate coercivity

DAI Li-li   

  1. School of Mathematics, Tonghua Normal University, Tonghua Jilin 134002, China
  • Received:2018-08-01 Online:2019-07-25 Published:2019-07-18

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摘要： 通过运用截断方法研究了一类带有变指数的椭圆方程.先利用变指数情形下的Marcinkiewicz估计，在得到逼近解序列的截断函数先验估计的基础上，选取适当的检验函数对逼近解序列做出估计，以此得出这类椭圆方程在加权Sobolev空间中熵解的存在性.

关键词: 退化椭圆方程, 加权Sobolev空间, 变指数, 截断函数

Abstract: In this paper, we use the truncation method to investigate the existence of solutions for degenerate elliptic problems with variable exponent in weighted Sobolev spaces. With the help of the Marcinkiewicz estimate and using some a priori estimates for the sequence of solutions of the approximate problem, and we choose suitable test functions for the approximate equation and obtain the needed estimates. Then, we obtain the entropy solutions for the elliptic equation in weighted Sobolev spaces with a variable exponent.

Key words: degenerate elliptic equation, weighted Sobolev space, variable exponent, truncation function

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