Strichartz estimates for Maxwell equations in media: The fully anisotropic case
Analysis of PDEs
2022-11-30 v1
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.
Keywords
Cite
@article{arxiv.2211.16130,
title = {Strichartz estimates for Maxwell equations in media: The fully anisotropic case},
author = {Robert Schippa and Roland Schnaubelt},
journal= {arXiv preprint arXiv:2211.16130},
year = {2022}
}
Comments
40 pages