TY - JOUR
T1 - L q -estimates for stationary stokes system with coefficients measurable in one direction
AU - Dong, Hongjie
AU - Kim, Doyoon
N1 - Funding Information:
H. Dong was partially supported by the NSF under agreements 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).
Publisher Copyright:
© The Author(s).
PY - 2019/4/1
Y1 - 2019/4/1
N2 - We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori Ẇ 1 q-estimates for any q ∈ [2, ∞) when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a W 1 q-estimate and prove the solvability for any q ∈ (1, ∞) when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.
AB - We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori Ẇ 1 q-estimates for any q ∈ [2, ∞) when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a W 1 q-estimate and prove the solvability for any q ∈ (1, ∞) when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.
KW - Boundary value problem
KW - Measurable coefficients
KW - Stokes systems
UR - http://www.scopus.com/inward/record.url?scp=85065607278&partnerID=8YFLogxK
U2 - 10.1142/S1664360719500048
DO - 10.1142/S1664360719500048
M3 - Article
AN - SCOPUS:85065607278
SN - 1664-3607
VL - 9
JO - Bulletin of Mathematical Sciences
JF - Bulletin of Mathematical Sciences
IS - 1
M1 - 1950004
ER -