Back to Search Start Over

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

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

Authors :
Dong, Hongjie
Yang, Zhuolun
Zhu, Hanye
Publication Year :
2023

Abstract

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.<br />Comment: 37 pages, 1 figure

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2311.11541
Document Type :
Working Paper