Advanced Search
Article Contents
Article Contents

Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields

Abstract Related Papers Cited by
  • In this paper we prove a fundamental estimate for the weak solution of a degenerate elliptic system: $\nabla\times [\rho(x)\nabla\times H]=F$, $\nabla\cdot H=0$ in a bounded domain in $R^3$, where $\rho(x)$ is only assumed to be in $L^{\infty}$ with a positive lower bound. This system is the steady-state of Maxwell’s system for the evolution of a magnetic field $H$ under the influence of an external force $F$, where $\rho(x)$ represents the resistivity of the conductive material. By using Campanato type of techniques, we show that the weak solution to the system is Hölder continuous, which is optimal under the assumption. This result solves the regularity problem for the system under the minimum assumption on the coefficient. Some applications arising in inductive heating are presented.
    Mathematics Subject Classification: 35J45, 35J70.


    \begin{equation} \\ \end{equation}
  • 加载中

Article Metrics

HTML views() PDF downloads(130) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint