Global Strichartz estimates for an inhomogeneous Maxwell system

Abstract

We show global-in-time Strichartz estimates for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as $|x|\to \infty$ and a non-trapping condition. The proof is based on smoothing estimates in weighted $L^2$ spaces which follow from corresponding resolvent estimates for the underlying Helmholtz problem.

References in corpus (3)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• Time-harmonic solutions for Maxwell's equations in anisotropic media and Bochner-Riesz estimates with negative index for non-elliptic surfaces
• On quasilinear Maxwell equations in two dimensions