TY - JOUR
T1 - Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients
AU - Dong, Hongjie
AU - Kim, Doyoon
N1 - Funding Information:
H. Dong was partially supported by the NSF under agreement DMS-1056737 and 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).
PY - 2018/4/5
Y1 - 2018/4/5
N2 - 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 Lq-estimates for the system when the domain is the whole Euclidean space or a half space.
AB - 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 Lq-estimates for the system when the domain is the whole Euclidean space or a half space.
KW - Measurable coefficients
KW - Muckenhoupt weights
KW - Reifenberg flat domains
KW - Small mean oscillations
KW - Stokes system
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U2 - 10.1016/j.jde.2017.12.011
DO - 10.1016/j.jde.2017.12.011
M3 - Article
AN - SCOPUS:85038926071
VL - 264
SP - 4603
EP - 4649
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 7
ER -