Higher order parabolic systems with piecewise DMO and Hölder continuous coefficients

In this paper, we are concerned with divergence form, higher-order parabolic systems in a cylindrical domain with a finite number of subdomains. We establish $L_{\mathrm{\infty }}$ and Schauder estimates of solutions when the leading coefficients and the non-homogeneous term exhibit piecewise Dini mean oscillation and piecewise Hölder continuity, respectively. To the best of our knowledge, our results are new for higher-order elliptic and parabolic systems.