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Weighted L-q-estimates for stationary Stokes system with partially BMO coefficients
- Authors
- Dong, Hongjie; Kim, Doyoon
- Issue Date
- 5-4월-2018
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Stokes system; Reifenberg flat domains; Measurable coefficients; Small mean oscillations; Muckenhoupt weights
- Citation
- JOURNAL OF DIFFERENTIAL EQUATIONS, v.264, no.7, pp.4603 - 4649
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF DIFFERENTIAL EQUATIONS
- Volume
- 264
- Number
- 7
- Start Page
- 4603
- End Page
- 4649
- ISSN
- 0022-0396
- 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 Lq-estimates for the system when the domain is the whole Euclidean space or a half space. (C) 2017 Elsevier Inc. All rights reserved.
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