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CONORMAL DERIVATIVE PROBLEMS FOR STATIONARY STOKES SYSTEM IN SOBOLEV SPACES
- Authors
- Choi, Jongkeun; Dong, Hongjie; Kim, Doyoon
- Issue Date
- 5월-2018
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- Stokes system; Reifenberg flat domains; measurable coefficients; conormal derivative boundary condition
- Citation
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.38, no.5, pp.2349 - 2374
- Indexed
- SCIE
SCOPUS
- Journal Title
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
- Volume
- 38
- Number
- 5
- Start Page
- 2349
- End Page
- 2374
- ISSN
- 1078-0947
- Abstract
- 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 Poincare inequality on Reifenberg flat domains, the proof of which is of independent interest.
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