Strichartz estimates for Maxwell equations in media: The fully anisotropic case

2022/11/29 by Schippa, Robert, Schnaubelt, Roland · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.16130

Abstract

We prove Strichartz estimates for Maxwell equations in media in the fully anisotropic case with Hölder-continuous coefficients. To this end, we use the FBI transform to conjugate the problem to phase space. After reducing to a scalar estimate by means of a matrix symmetrizer, we show oscillatory integral estimates for a variable-coefficient Fourier extension operator. The characteristic surface has conical singularities for any non-vanishing time frequency. Combined with energy estimates, we improve the local well-posedness for certain fully anisotropic quasilinear Maxwell equations.

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• Decay estimates of wave equations in un-isotropic media

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