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arXiv · 2211.16130

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

Robert Schippa·Roland Schnaubelt
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Abstract

We prove Strichartz estimates for Maxwell equations in media in the fully anisotropic case with H\"older-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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Robert Schippa, Roland Schnaubelt. 2022-11-29. Strichartz estimates for Maxwell equations in media: The fully anisotropic case. https://arxiv.org/abs/2211.16130

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