Conormal derivative problems for stationary stokes system in Sobolev spaces

Jongkeun Choi, Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We prove the solvability in Sobolev spaces of the conormal derivative problem for the stationary Stokes system with irregular coefficients on bounded Reifenberg flat domains. The coefficients are assumed to be merely measurable in one direction, which may differ depending on the local coordinate systems, and have small mean oscillations in the other directions. In the course of the proof, we use a local version of the Poincaré inequality on Reifenberg flat domains, the proof of which is of independent interest.

Original languageEnglish
Pages (from-to)2349-2374
Number of pages26
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume38
Issue number5
DOIs
Publication statusPublished - 2018 May 1

Keywords

  • Conormal derivative boundary condition
  • Measurable coefficients
  • Reifenberg flat domains
  • Stokes system

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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