Conormal derivative problems for stationary Stokes system in Sobolev spaces

2017/08/18 by Jongkeun Choi, Hongjie Dong, Choi, Jongkeun +3
Computer Science · Mathematics · #35G45 #35R05 #76D07 #76N10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1708.05497

openalex publication_date 2017/08/18 · openalex created_date 2017/08/31 · openalex updated_date 2026/07/28

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.

Related

• Green functions for stationary Stokes systems with conormal derivative boundary condition in two dimensions
• Green functions of mixed boundary value problems for stationary Stokes systems in two dimensions
• Weighted L_q-estimates for stationary Stokes system with partially BMO coefficients
• The conormal derivative problem for higher order elliptic systems with irregular coefficients
• L_q-estimates for stationary Stokes system with coefficients measurable in one direction