Abstract
The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.
Original language | English |
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Pages (from-to) | 3279-3327 |
Number of pages | 49 |
Journal | Journal of Functional Analysis |
Volume | 261 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2011 Dec 1 |
Externally published | Yes |
Keywords
- Higher order systems
- Partially small BMO coefficients
- Sobolev spaces
- Vanishing mean oscillation
ASJC Scopus subject areas
- Analysis