Lp estimates of time-harmonic Maxwellʹs equations in a bounded domain

Consider the electromagnetic field scattered by a nonlinear bounded optical medium. Because of inhomogeneity of the medium, the governing equations are Maxwellʹs 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, Lp estimates for Maxwellʹs equation with jump coefficients are established. The solution of Maxwellʹs equation is represented by spherical harmonics. An application of the Lp estimates gives rise to the well-posedness of a linearized model.