Strichartz estimates for Maxwell equations in media: the structured case in two dimensions

We prove Strichartz estimates for the two dimensional Maxwell equations with diagonal Lipschitz permittivity of special structure. The estimates have no loss in regularity that occurs in general for C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document}-coefficients. In the charge-free case, we recover Strichartz estimates local-in-time for Euclidean wave equations in two dimensions up to endpoints.