An $H^{s,p}(\curl;\Omega)$ estimate for the Maxwell system

Abstract

We derive an $H_{0}^{s,p}(\curl;\Omega)$ estimate for the solutions of the Maxwell type equations modeled with anisotropic and $W^{s, \infty}(\Omega)$-regular coefficients. Here, we obtain the regularity of the solutions for the integrability and smoothness indices $(p, s)$ in a plan domain characterized by the apriori lower/upper bounds of $a$ and the apriori upper bound of its H{\"o}lder semi-norm of order $s$. The proof relies on a perturbation argument generalizing Gr{\"o}ger's $L^p$-type estimate, known for the elliptic problems, to the Maxwell system.