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


    • Division of Applied MathematicsBrown University
  • Doyoon Kim
    • Department of Applied MathematicsKyung Hee University

DOI: 10.1007/s00205-010-0345-3

Cite this article as:
Dong, H. & Kim, D. Arch Rational Mech Anal (2011) 199: 889. doi:10.1007/s00205-010-0345-3


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.

Copyright information

© Springer-Verlag 2010