We study the limiting absorption principle and the well-posedness of Maxwell equations with anisotropic sign-changing coefficients in the time-harmonic domain. The starting point of the analysis is to obtain Cauchy problems associated with two Maxwell systems using a change of variables. We then derive a priori estimates for these Cauchy problems using two different approaches. The Fourier approach involves the complementing conditions for the Cauchy problems associated with two elliptic equations, which were studied in a general setting by Agmon, Douglis, and Nirenberg. The variational approach explores the variational structure of the Cauchy problems of the Maxwell equations. As a result, we obtain general conditions on the coefficients for which the limiting absorption principle and the well-posedness hold. Moreover, these {\it new} conditions are of a local character and easy to check. Our work is motivated by and provides general sufficient criteria for the stability of electromagnetic fields in the context of negative-index metamaterials.

中文翻译：

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具有各向异性符号变化系数的时谐麦克斯韦方程的限制吸收原理和适定性

我们研究了时谐域中具有各向异性符号变化系数的麦克斯韦方程组的极限吸收原理和适定性。分析的起点是使用变量的变化获得与两个麦克斯韦系统相关的柯西问题。然后我们使用两种不同的方法对这些柯西问题进行先验估计。傅立叶方法涉及与两个椭圆方程相关的柯西问题的补充条件，Agmon、Douglis 和 Nirenberg 在一般环境中研究了这些问题。变分方法探索麦克斯韦方程的柯西问题的变分结构。结果，我们获得了限制吸收原理和适定性成立的系数的一般条件。而且，这些 {\it new} 条件具有本地特征并且易于检查。我们的工作受到负折射率超材料背景下电磁场稳定性的启发并提供了普遍的充分标准。