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

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

36 Citations (Scopus)

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 languageEnglish
Pages (from-to)3279-3327
Number of pages49
JournalJournal of Functional Analysis
Volume261
Issue number11
DOIs
Publication statusPublished - 2011 Dec 1

Keywords

  • Higher order systems
  • Partially small BMO coefficients
  • Sobolev spaces
  • Vanishing mean oscillation

ASJC Scopus subject areas

  • Analysis

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