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

Abstract

We derive an $H_{0}^{s,p}(\curl;Ω)$ 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{ö}lder semi-norm of order $s$. The proof relies on a perturbation argument generalizing Gr{ö}ger's $L^p$-type estimate, known for the elliptic problems, to the Maxwell system.

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