  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.
