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We prove the solvability in Sobolev spaces for both divergence andnon-divergence form higher order parabolic and elliptic systems in the wholespace, on a half space, and on a bounded domain. The leading coefficients areassumed to be merely measurable in the time variable and have small meanoscillations with respect to the spatial variables in small balls or cylinders.For the proof, we develop a set of new techniques to produce mean oscillationestimates for systems on a half space.

On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients