一类带有退化强制项的奇异椭圆方程解的存在性

数学物理学报 ›› 2017, Vol. 37 ›› Issue (5): 877-894.

一类带有退化强制项的奇异椭圆方程解的存在性

李清微¹, 高文杰², 韩玉柱²

1. 大连海事大学数学系辽宁大连 116000;
2. 吉林大学数学学院长春 130012

收稿日期:2016-12-15 修回日期:2017-05-07 出版日期:2017-10-26 发布日期:2017-10-26
作者简介:李清微,E-mail:yzhan@jlu.edu.cn
基金资助:
国家自然科学基金（11401252）、吉林省科技厅青年基金（20160520103JH）和吉林省教育厅科研基金（2015-463）

Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity

Li Qingwei¹, Gao Wenjie², Han Yuzhu²

1. Department of Mathematics, Dalian Maritime University, Liaoning Dalian 116000;
2. School of Mathematics, Jilin University, Changchun 130012

Received:2016-12-15 Revised:2017-05-07 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by the NSFC (11401252), the Natural Science Foundation of Jilin Province (20160520103JH) and the Scientific Research Project of the Education Department of Jilin Province (2015-463)

摘要/Abstract

摘要： 该文研究了一类具退化强制项和自然增长条件梯度项的奇异椭圆方程的Dirichlet边值问题
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其中，Ω⊂R^N（N ≥p）是一有界区域，B，γ，θ>0，p>1，f是某一Lebesgue空间L^m（Ω）（m ≥1）中的非负函数.利用截断技术并结合选取适当的检验函数，证明了该问题非负解的存在性以及正则性等结果.该文结果表明尽管低阶梯度项是奇异的，它的存在对解的正则性有"好"的影响.

关键词: 退化强制, 奇异性, 低阶梯度项, 存在, 正则性

Abstract: In this article, the authors consider the existence of solutions for the following elliptic boundary value problem with degenerate coercivity and a singular lower order term with natural growth with respect to the gradient of the following form
???20170509???,
where Ω⊂R^N(N ≥ p) is a bounded domain, B,γ,θ>0 and p > 1, and f is a non-negative function belonging to some Lebesgue space L^m(Ω) with m ≥ 1. By combining the truncation methods with several delicate test functions, the existence and regularity of solution is proved. The results show that the lower order term has some regularizing effects on the solution, even if it is singular.

Key words: Degenerate coercivity, Singularity, Lower order term, Existence, Regularity

中图分类号:

O175.2

李清微, 高文杰, 韩玉柱. 一类带有退化强制项的奇异椭圆方程解的存在性[J]. 数学物理学报, 2017, 37(5): 877-894.

Li Qingwei, Gao Wenjie, Han Yuzhu. Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity[J]. Acta mathematica scientia,Series A, 2017, 37(5): 877-894.

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