Archive for Rational Mechanics and Analysis

, Volume 199, Issue 3, pp 889-941

First online:

On the L p -Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients

  • Hongjie DongAffiliated withDivision of Applied Mathematics, Brown University Email author 
  • , Doyoon KimAffiliated withDepartment of Applied Mathematics, Kyung Hee University

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