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Asymptotics of the solution to the perfect conductivity problem with $p$-Laplacian
Asymptotics of the solution to the perfect conductivity problem with $p$-Laplacian
- 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
- Subjects :
- Mathematics - Analysis of PDEs
35B40, 35J92, 35Q74, 74E30, 74G70
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2311.11541
- Document Type :
- Working Paper