Lp solvability of divergence type parabolic and elliptic systems with partially BMO coefficients

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

We prove the Hp,q 1 solvability of second order systems in divergence form with leading coefficients Aαβ only measurable in (t, x1) and having small BMO (bounded mean oscillation) semi-norms in the other variables. In addition, we assume one of the following conditions is satisfied: (i) A11 is measurable in t and has a small BMO semi-norm in the other variables; (ii) A11 is measurable in x1 and has a small BMO semi-norm in the other variables. The corresponding results for the Cauchy problem and elliptic systems are also established. Some of our results are new even for scalar equations. Using the results for systems in the whole space, we obtain the solvability of systems on a half space and Lipschitz domain with either the Dirichlet boundary condition or the conormal derivative boundary condition.

Original languageEnglish
Pages (from-to)357-389
Number of pages33
JournalCalculus of Variations and Partial Differential Equations
Volume40
Issue number3
DOIs
Publication statusPublished - 2011 Jan 1
Externally publishedYes

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Bounded Mean Oscillation
Seminorm
Parabolic Systems
Elliptic Systems
Type Systems
Solvability
Divergence
Boundary conditions
Coefficient
Lipschitz Domains
Second-order Systems
Derivatives
Half-space
Dirichlet Boundary Conditions
Cauchy Problem
Scalar
Derivative

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Lp solvability of divergence type parabolic and elliptic systems with partially BMO coefficients. / Dong, Hongjie; Kim, Doyoon.

In: Calculus of Variations and Partial Differential Equations, Vol. 40, No. 3, 01.01.2011, p. 357-389.

Research output: Contribution to journalArticle

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