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浙江大学学报（理学版）
浙江大学学报（理学版）  2018, Vol. 45 Issue (6): 673-678    DOI: 10.3785/j.issn.1008-9497.2018.06.005
数学与计算机科学     
一类具退化强制的椭圆方程在加权Sobolev空间中重整化解的存在性
代丽丽
通化师范学院 数学学院, 吉林 通化 134002
Existence of renormalized solutions for a degenerate elliptic equation with degenerate coercivity in weighted Sobolev spaces
DAI Lili
Institute of Mathematics, Tonghua Normal University, Tonghua 134002, Jilin Province, China
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摘要： 运用截断方法研究了一类椭圆方程在加权Sobolev空间中解的存在性.主要采用Marcinkiewicz估计，在得到逼近解序列的截断函数先验估计的基础上，通过选取适当的检验函数，对逼近解序列做合适的估计，以此证明重整化解的存在性.
关键词： 退化椭圆方程;  截断函数;  加权Sobolev空间;  权函数    
Abstract: In this paper, we consider the following nonlinear elliptic equation with degenerate coercivity and lower order term in the setting of the weighted Sobolev space. We investigate the existence of the renormalized solutions in W01,p(Ω,ω) by the truncation method. With the help of Marcinkiewicz estimate, through some priori estimates for the sequence of solutions of the approximate problem, we prove that un converges in measure. Then we choose suitable test functions for the approximate equation and obtain the needed estimates. Finally, through a limit process, we obtain the existence of renormalized solutions to problem.
Key words: degenerate elliptic equation    truncation function    weighted Sobolev space    weighted functions
收稿日期: 2017-09-22 出版日期: 2018-11-25
CLC:  O175.2  
基金资助: 吉林省科技厅青年科研基金项目（20160520103JH）；吉林省教育厅科研项目（吉教科合字[2015]第441号）.
作者简介: 代丽丽(1982-),ORCID:http://orcid.org/0000-0002-6376-6949,女,博士,讲师,主要从事偏微分方程及其应用研究,E-mail:drx820115@126.com.
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引用本文:

代丽丽. 一类具退化强制的椭圆方程在加权Sobolev空间中重整化解的存在性[J]. 浙江大学学报（理学版）, 2018, 45(6): 673-678.

DAI Lili. Existence of renormalized solutions for a degenerate elliptic equation with degenerate coercivity in weighted Sobolev spaces. Journal of Zhejiang University (Science Edition), 2018, 45(6): 673-678.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.06.005    或    https://www.zjujournals.com/sci/CN/Y2018/V45/I6/673

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