TY - JOUR
T1 - Conormal derivative problems for stationary stokes system in Sobolev spaces
AU - Choi, Jongkeun
AU - Dong, Hongjie
AU - Kim, Doyoon
N1 - Funding Information:
J. Choi was supported by a Korea University Grant. H. Dong was partially supported by the NSF under agreement DMS-1600593. D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03934369).
Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.
PY - 2018/5
Y1 - 2018/5
N2 - 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.
AB - 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.
KW - Conormal derivative boundary condition
KW - Measurable coefficients
KW - Reifenberg flat domains
KW - Stokes system
UR - http://www.scopus.com/inward/record.url?scp=85043574283&partnerID=8YFLogxK
U2 - 10.3934/dcds.2018097
DO - 10.3934/dcds.2018097
M3 - Article
AN - SCOPUS:85043574283
SN - 1078-0947
VL - 38
SP - 2349
EP - 2374
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 5
ER -