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2006 Regularity of weak solution to a $p$-curl-system
Hong-Ming Yin
Differential Integral Equations 19(4): 361-368 (2006).

Abstract

In this note we study the regularity of weak solutions to a nonlinear steady-state Maxwell's equation in conductive media: $\nabla\times \big[|{\nabla \times }{{\bf H}}|^{p-2} \nabla \times {{\bf H}} \big]={ {\bf F} }(x), p>1, $ where ${{\bf H}}(x)$ represents the magnetic field while ${ {\bf F} }(x)$ is the internal magnetic current. It is shown that the weak solution to the above system is of class $C^{1+\alpha}$, which is optimal. The basic idea is to introduce a suitable potential and then to transform the system into a $p-$Laplacian equation subject to a Neumann type of boundary condition. The desired regularity is established by using the known theory for the scalar p-Laplacian equation.

Citation

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Hong-Ming Yin. "Regularity of weak solution to a $p$-curl-system." Differential Integral Equations 19 (4) 361 - 368, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35472
MathSciNet: MR2215624

Subjects:
Primary: 35Q60
Secondary: 35D10 , 35J50 , 49N60 , 78A25

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 4 • 2006
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