具有 p 拉普拉卡矩的完美传导性问题解的渐近性

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-04-30 DOI:10.1007/s00208-024-02876-y

Hongjie Dong, Zhuolun Yang, Hanye Zhu

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引用次数: 0

摘要

我们研究的是完美导体嵌入同质矩阵中的完美导体问题，其中电流-电场关系为幂律 \(J=\sigma|E|^{p-2}E\)。当夹杂物之间的距离（\(\varepsilon \)）趋近于 0 时，解的梯度可以任意大。这是关于非线性完全导电性问题的第一个梯度渐近学结果。

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Asymptotics of the solution to the perfect conductivity problem with p-Laplacian

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Asymptotics of the solution to the perfect conductivity problem with p-Laplacian

We study the perfect conductivity problem with closely spaced perfect conductors embedded in a homogeneous matrix where the current-electric field relation is the power law \(J=\sigma |E|^{p-2}E\). The gradient of solutions may be arbitrarily large as \(\varepsilon \), the distance between inclusions, approaches to 0. To characterize this singular behavior of the gradient in the narrow region between two inclusions, we capture the leading order term of the gradient. This is the first gradient asymptotics result on the nonlinear perfect conductivity problem.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.