Conormal derivative problems for stationary Stokes system in Sobolev spaces

Jongkeun Choi; Hongjie Dong; Doyoon Kim

doi:10.3934/dcds.2018097

Article Contents

2018, Volume 38, Issue 5: 2349-2374. Doi: 10.3934/dcds.2018097

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Conormal derivative problems for stationary Stokes system in Sobolev spaces

1.
Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea
2.
Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA

^* Corresponding author: Doyoon Kim
^* Corresponding author: Doyoon Kim

Received: July 31, 2017

Published: June 2018

J. Choi was supported by a Korea University Grant. H. Dong was partially supported by the NSF under agreement 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)

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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 Poincaré inequality on Reifenberg flat domains, the proof of which is of independent interest.

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Mathematics Subject Classification: 35R05, 76N10, 76D07, 35G45.

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