Weighted L q -estimates for stationary Stokes system with partially BMO coefficients

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

10 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 languageEnglish
Pages (from-to)4603-4649
Number of pages47
JournalJournal of Differential Equations
Volume264
Issue number7
DOIs
Publication statusPublished - 2018 Apr 5

Fingerprint

Stokes System
Sobolev spaces
Unique Solvability
Coefficient
Estimate
Weighted Sobolev Spaces
Half-space
Sobolev Spaces
Euclidean space
Oscillation

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Weighted L q -estimates for stationary Stokes system with partially BMO coefficients . / Dong, Hongjie; Kim, Doyoon.

In: Journal of Differential Equations, Vol. 264, No. 7, 05.04.2018, p. 4603-4649.

Research output: Contribution to journalArticle

@article{266f516a6db8409783e366e6309970cd,
title = "Weighted L q -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 L q -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",
year = "2018",
month = "4",
day = "5",
doi = "10.1016/j.jde.2017.12.011",
language = "English",
volume = "264",
pages = "4603--4649",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "7",

}

TY - JOUR

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

AU - Dong, Hongjie

AU - Kim, Doyoon

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 L q -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 L q -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

UR - http://www.scopus.com/inward/record.url?scp=85038926071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038926071&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2017.12.011

DO - 10.1016/j.jde.2017.12.011

M3 - Article

AN - SCOPUS:85038926071

VL - 264

SP - 4603

EP - 4649

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 7

ER -