Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients

Hongjie Dong; Doyoon Kim

doi:10.1016/j.jde.2017.12.011

Weighted L_q-estimates for stationary Stokes system with partially BMO coefficients

Hongjie Dong, Doyoon Kim

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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 L_q-estimates for the system when the domain is the whole Euclidean space or a half space.

Original language	English
Pages (from-to)	4603-4649
Number of pages	47
Journal	Journal of Differential Equations
Volume	264
Issue number	7
DOIs	https://doi.org/10.1016/j.jde.2017.12.011
Publication status	Published - 2018 Apr 5

Keywords

Measurable coefficients
Muckenhoupt weights
Reifenberg flat domains
Small mean oscillations
Stokes system

ASJC Scopus subject areas

Analysis
Applied Mathematics

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@article{266f516a6db8409783e366e6309970cd,

title = "Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients",

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.",

keywords = "Measurable coefficients, Muckenhoupt weights, Reifenberg flat domains, Small mean oscillations, Stokes system",

author = "Hongjie Dong and Doyoon Kim",

note = "Funding Information: H. Dong was partially supported by the NSF under agreement 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).",

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doi = "10.1016/j.jde.2017.12.011",

language = "English",

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journal = "Journal of Differential Equations",

issn = "0022-0396",

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T1 - Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients

AU - Dong, Hongjie

AU - Kim, Doyoon

N1 - Funding Information: H. Dong was partially supported by the NSF under agreement 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).

PY - 2018/4/5

Y1 - 2018/4/5

N2 - 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.

AB - 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.

KW - Measurable coefficients

KW - Muckenhoupt weights

KW - Reifenberg flat domains

KW - Small mean oscillations

KW - Stokes system

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

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