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

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)889-941
Number of pages53
JournalArchive for Rational Mechanics and Analysis
Volume199
Issue number3
DOIs
Publication statusPublished - 2011 Jan 1
Externally publishedYes

Fingerprint

Sobolev spaces
Parabolic Systems
Elliptic Systems
Half-space
Solvability
Oscillation
Higher Order
Coefficient
Sobolev Spaces
Bounded Domain
Divergence
Ball
Estimate
Form

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

On the Lp-Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients. / Dong, Hongjie; Kim, Doyoon.

In: Archive for Rational Mechanics and Analysis, Vol. 199, No. 3, 01.01.2011, p. 889-941.

Research output: Contribution to journalArticle

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