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浙江大学学报（理学版）
浙江大学学报（理学版）  2023, Vol. 50 Issue (1): 25-29    DOI: 10.3785/j.issn.1008-9497.2023.01.004
数学与计算机科学     
一类非齐次椭圆方程组非常弱解的正则性
陈淑红()
武夷学院 数学与计算机学院，福建 武夷山 354300
Regularity of very weak solutions for a class of inhomogeneous elliptic equations
Shuhong CHEN()
School of Mathematics and Computer，Wuyi University，Wuyishan 354300，Fujian Province，China
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摘要：

研究一类非齐次项是p-Laplace算子的椭圆方程组非常弱解的正则性。结合Hodge分解以及偏微分方程正则性理论的证明技巧，建立了具有p-Laplace型椭圆方程组的非常弱解与经典意义下的弱解之间的关系。
关键词： p-Laplace型;  非常弱解;  Hodge分解;  正则性    
Abstract:

In this paper, we study the regularity theory of very weak solutions for a class of elliptic equations which inhomogeneous terms are p-Laplace operators. Combining Hodge decomposition and the regularity theory of partial differential equations, the relation between the very weak solution of p-Laplacian elliptic equations and the weak solution in the classical sense is established.
Key words: p-Laplace type    very weak solution    Hodge decomposition    regularity
收稿日期: 2021-09-09 出版日期: 2023-01-13
CLC:  O 175.2  
基金资助: 国家自然科学基金资助项目(11571159);武夷学院引进人才科研启动项目(YJ202118)
作者简介: 陈淑红（1979—），ORCID：https：//orcid.org/0000-0001-6648-6486，女，博士（后），教授，主要从事偏微分方程研究，E-mail：shiny0320@163.com.
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引用本文:

陈淑红. 一类非齐次椭圆方程组非常弱解的正则性[J]. 浙江大学学报（理学版）, 2023, 50(1): 25-29.

Shuhong CHEN. Regularity of very weak solutions for a class of inhomogeneous elliptic equations. Journal of Zhejiang University (Science Edition), 2023, 50(1): 25-29.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2023.01.004    或    https://www.zjujournals.com/sci/CN/Y2023/V50/I1/25

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