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\(L^p\) estimates of time-harmonic Maxwell’s equations in a bounded domain. (English) Zbl 1151.78009

Summary: Consider the electromagnetic field scattered by a nonlinear bounded optical medium. Because of inhomogeneity of the medium, the governing equations are Maxwell’s equation with jump coefficients and a source term. By using the Sommerfeld radiation condition, the model scattering problem may be truncated into a bounded domain. In this paper, \(L^p\) estimates for Maxwell’s equation with jump coefficients are established. The solution of Maxwell’s equation is represented by spherical harmonics. An application of the \(L^p\) estimates gives rise to the well-posedness of a linearized model.

MSC:

78A45 Diffraction, scattering
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