Weighted L q -estimates for stationary Stokes system with partially BMO coefficients

Hongjie Dong, Doyoon Kim

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10 Citations (Scopus)

Abstract

We prove the unique solvability of solutions in Sobolev spaces to the stationary Stokes system on a bounded Reifenberg flat domain when the coefficients are partially BMO functions, i.e., locally they are merely measurable in one direction and have small mean oscillations in the other directions. Using this result, we establish the unique solvability in Muckenhoupt type weighted Sobolev spaces for the system with partially BMO coefficients on a Reifenberg flat domain. We also present weighted a priori L q -estimates for the system when the domain is the whole Euclidean space or a half space.

Original languageEnglish
Pages (from-to)4603-4649
Number of pages47
JournalJournal of Differential Equations
Volume264
Issue number7
DOIs
Publication statusPublished - 2018 Apr 5

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Keywords

  • Measurable coefficients
  • Muckenhoupt weights
  • Reifenberg flat domains
  • Small mean oscillations
  • Stokes system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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