| 具有强奇性的半线性椭圆方程 |
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| 作者姓名： | 谭玉鑫 孙义静 |
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| 作者单位： | 中国科学院大学数学科学学院, 北京 100049 |
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| 基金项目： | Supported by the National Nature Science Foundation of China (11571339) |
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| 摘 要： | 证明-div（M（x）▽u）=（f（x））/（up）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。
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| 关 键 词： | 有界椭圆矩阵 弱解 强奇性 |
| 收稿时间： | 2016-09-07 |
| 修稿时间： | 2016-12-19 |
Semilinear elliptic equations with strong singularity |
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| Authors: | TAN Yuxin SUN Yijing |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | We prove the existence of a positive H01-solution for the equation-div(M(x) ▽u)=(f(x))/(up), 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. |
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| Keywords: | bounded elliptic matrix weak solution strong singularity |
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