arXiv 1102.14892011-02-08math.AP

Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

Hongjie Dong, Doyoon Kim

备注：: 45 pages, submitted in Nov. 2010
发表信息：: Journal of Functional Analysis (2011), 261 (11), 3279-3327
DOI：: 10.1016/j.jfa.2011.08.001

英文摘要：

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.

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