具有强奇性的半线性椭圆方程

doi:10.7523/j.issn.2095-6134.2017.06.002

中国科学院大学学报 ›› 2017, Vol. 34 ›› Issue (6): 660-666.DOI: 10.7523/j.issn.2095-6134.2017.06.002

具有强奇性的半线性椭圆方程

谭玉鑫, 孙义静

中国科学院大学数学科学学院, 北京 100049

收稿日期:2016-09-07 修回日期:2016-12-19 发布日期:2017-11-15
通讯作者: 谭玉鑫
基金资助:
Supported by the National Nature Science Foundation of China (11571339)

Semilinear elliptic equations with strong singularity

TAN Yuxin, SUN Yijing

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2016-09-07 Revised:2016-12-19 Published:2017-11-15
Supported by:
Supported by the National Nature Science Foundation of China (11571339)

摘要/Abstract

摘要： 证明-div（M（x）▽u）=（f（x））/（u^p）正H₀¹-解的存在性，其中M（x）是有界椭圆矩阵（即存在0< α ≤ β满足M（x）ξ·ξ ≥ α|ξ|²，|M（x）|≤ β，∀x ∈ Ω，∀ξ ∈ Rⁿ）和-p <-1.本工作的关键点在于建立2个密切联系的集合，便于找到相应的能量泛函最小值。

关键词: 有界椭圆矩阵, 弱解, 强奇性

Abstract: We prove the existence of a positive H₀¹-solution for the equation-div(M(x) ▽u)=(f(x))/(u^p), where M(x) is a bounded elliptic matrix (i. e., there exists 0< α ≤ β such that M(x)ξ·ξ ≥ α|ξ|²,|M(x)|≤ β,∀x ∈ Ω,∀ξ ∈ Rⁿ), and-p <-1. The key to the work lies in establishing the validity and connection of two constraints which simplify the existence of a minimizer for the corresponding singular functional.

Key words: bounded elliptic matrix, weak solution, strong singularity

中图分类号:

O175.25

谭玉鑫, 孙义静. 具有强奇性的半线性椭圆方程[J]. 中国科学院大学学报, 2017, 34(6): 660-666.

TAN Yuxin, SUN Yijing. Semilinear elliptic equations with strong singularity[J]. , 2017, 34(6): 660-666.

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具有强奇性的半线性椭圆方程

Semilinear elliptic equations with strong singularity

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