Archive for Rational Mechanics and Analysis

, Volume 199, Issue 3, pp 889–941

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



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.


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of Applied MathematicsKyung Hee UniversityGyeonggi-doKorea

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