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浙江大学学报(理学版)  2020, Vol. 47 Issue (1): 77-80    DOI: 10.3785/j.issn.1008-9497.2020.01.011
数学与计算机科学     
一个带权函数的拟线性椭圆方程的有界弱解
李仲庆
贵州财经大学 数统学院,贵州 贵阳 550025
Bounded weak solutions to a quasi-linear elliptic equation with weight function
LI Zhongqing
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
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摘要: 在经典的 Sobolev 空间框架中, 运用 De Giorgi 迭代技术, 给出了一个带权的非线性椭圆方程弱解的先验L估计。基于最大模估计, 用偏微分方程中的弱收敛方法及极限过程, 证明了弱解的存在性。
关键词: 非线性椭圆方程权函数最大模估计    
Abstract: In the framework of the classical Sobolev spaces, by adopting the De Giorgi iteration technique, the L estimate to a nonlinear elliptic equation with weight function is given. Based upon the maximal norm estimate, employing the weak convergence methods in PDEs, the existence of weak solutions is proved by the limit process.
Key words: nonlinear elliptic equations    weight function    maximal norm estimate
收稿日期: 2018-11-01 出版日期: 2020-01-25
CLC:  O175.8  
基金资助: 国家自然科学基金(青年科学基金) 资助项目(11401252);2019年度贵州财经大学校级科研基金项目(2019XYB08).
作者简介: 李仲庆(1984—),ORCID:https://orcid.org/0000-0002-2152-8985,男,博士,讲师,主要从事偏微分方程研究.
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引用本文:

李仲庆. 一个带权函数的拟线性椭圆方程的有界弱解[J]. 浙江大学学报(理学版), 2020, 47(1): 77-80.

LI Zhongqing. Bounded weak solutions to a quasi-linear elliptic equation with weight function. Journal of Zhejiang University (Science Edition), 2020, 47(1): 77-80.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.01.011        https://www.zjujournals.com/sci/CN/Y2020/V47/I1/77

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