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

2021/08/17 by Robert Schippa, Schippa, Robert
Engineering · Mathematics · #35B64 #Advanced Mathematical Physics Problems #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Primary: 35L45 #Secondary: 35Q61

paper · pdf · doi:10.48550/arxiv.2108.07691

openalex publication_date 2021/08/17 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase space. We use the Strichartz estimates in a known combination with energy estimates to show the new well-posedness results for quasilinear Maxwell equations.

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