doi:10.12202/j.0476-0301.2020037潘星辰^{1, 2},
保继光^2,,
1.山东省青岛第六中学，266515，山东青岛
2.北京师范大学数学科学学院，100875，北京

详细信息 中图分类号:O175.2

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收稿日期:2020-02-28
网络出版日期:2020-07-22
刊出日期:2020-10-31

A perfect form of inhomogeneous elliptic equations

Xingchen PAN^{1, 2},
Jiguang BAO^2,,
1. Qingdao No.6 middle school, Shandong Province, 266515, Qingdao, Shandong，China
2. School of Mathematical Sciences, Beijing Normal University, 100875, Beijing, China
Funds:The authors are supported in part by the National Natural Science Foundation of China (11871102)

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Corresponding author:Bao Jiguang, man, doctor. Research direction: partial differential equation. e-mail: jgbao@bnu.edu.cn

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摘要
摘要:从传导问题中获得了一类非齐次椭圆方程Dirichlet问题的极限形式. 当2个理想导体之间的距离足够小时, 建立其最优的全局梯度估计, 从而给出了电场强度的爆破率.
关键词:分片常系数/
非齐次椭圆方程/
超导问题/
最优的梯度估计
Abstract:Limit form of a class of non-homogeneous elliptic equation Dirichlet problems is obtained from conduction problem, to establish optimal global gradient estimate when distance between two perfect conductors is small enough. Blow-up rates of electric field strength are given in all dimensions.
Key words:piecewise-constant coefficients/
inhomogeneous elliptic equation/
limiting form/
optimal gradient estimates