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

By Hongjie Dong, Doyoon Kim. 2010

124 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/5d2fd954452f706eafafd329601f43f146448748

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In Applied Mathematics

1. Hongjie Dong
2. Doyoon Kim

Citations in the corpus

• L-estimates for time fractional parabolic equations with coefficients measurable in time (2018, background): “2), it is possible to consider more general classes of coefficients than those in [7, 8, 4].”