Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients |
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Authors: | Hongjie Dong Doyoon Kim |
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Affiliation: | 1. Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA;2. Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea |
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Abstract: | 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 -estimates for the system when the domain is the whole Euclidean space or a half space. |
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Keywords: | 35R05 76N10 76D07 Stokes system Reifenberg flat domains Measurable coefficients Small mean oscillations Muckenhoupt weights |
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