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

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.

45 pages, submitted in Nov. 2010

References in corpus (2)

• Elliptic equations in divergence form with partially BMO coefficients
• On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients

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