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

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

2010-03-04

arxiv.org/abs/1003.0969v2

Mathematics

Analysis of PDEs

44 pages, introduction revised, references expanded. To appear in Arch. Rational Mech. Anal

Scientific paper

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 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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