Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain

Jongkeun Choi; Hongjie Dong; Zongyuan Li

doi:10.1007/s00245-019-09600-2

Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain

Jongkeun Choi, Hongjie Dong^*, Zongyuan Li

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

8 Citations (Scopus)

Abstract

We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique W^1,^p solvability is obtained with p being in the optimal range (4/3, 4). The leading coefficients are assumed to have small mean oscillations and the boundary of domain is Reifenberg flat. We also assume that the two boundary conditions are separated by some Reifenberg flat set of co-dimension 2 on the boundary. © Springer Science+Business Media, LLC, part of Springer Nature 2019.

Original language	English
Pages (from-to)	1547-1583
Journal	Applied Mathematics & Optimization
Volume	83
Issue number	3
Online published	31 Jul 2019
DOIs	https://doi.org/10.1007/s00245-019-09600-2
Publication status	Published - Jun 2021
Externally published	Yes

Research Keywords

Mixed boundary value problem
Second-order elliptic equations of divergence form
Reifenberg flat domains
W1,p estimate and solvability

Access Output

10.1007/s00245-019-09600-2

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{19a7ad9892594e698eee3d11d8ad86e1,

title = "Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain",

abstract = "We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique W1,p solvability is obtained with p being in the optimal range (4/3, 4). The leading coefficients are assumed to have small mean oscillations and the boundary of domain is Reifenberg flat. We also assume that the two boundary conditions are separated by some Reifenberg flat set of co-dimension 2 on the boundary. {\textcopyright} Springer Science+Business Media, LLC, part of Springer Nature 2019.",

keywords = "Mixed boundary value problem, Second-order elliptic equations of divergence form, Reifenberg flat domains, W1,p estimate and solvability",

author = "Jongkeun Choi and Hongjie Dong and Zongyuan Li",

year = "2021",

month = jun,

doi = "10.1007/s00245-019-09600-2",

language = "English",

volume = "83",

pages = "1547--1583",

journal = "Applied Mathematics & Optimization",

issn = "0095-4616",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain

AU - Choi, Jongkeun

AU - Dong, Hongjie

AU - Li, Zongyuan

PY - 2021/6

Y1 - 2021/6

N2 - We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique W1,p solvability is obtained with p being in the optimal range (4/3, 4). The leading coefficients are assumed to have small mean oscillations and the boundary of domain is Reifenberg flat. We also assume that the two boundary conditions are separated by some Reifenberg flat set of co-dimension 2 on the boundary. © Springer Science+Business Media, LLC, part of Springer Nature 2019.

AB - We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique W1,p solvability is obtained with p being in the optimal range (4/3, 4). The leading coefficients are assumed to have small mean oscillations and the boundary of domain is Reifenberg flat. We also assume that the two boundary conditions are separated by some Reifenberg flat set of co-dimension 2 on the boundary. © Springer Science+Business Media, LLC, part of Springer Nature 2019.

KW - Mixed boundary value problem

KW - Second-order elliptic equations of divergence form

KW - Reifenberg flat domains

KW - W1,p estimate and solvability

UR - http://www.scopus.com/inward/record.url?scp=85069969963&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85069969963&origin=recordpage

U2 - 10.1007/s00245-019-09600-2

DO - 10.1007/s00245-019-09600-2

M3 - RGC 21 - Publication in refereed journal

SN - 0095-4616

VL - 83

SP - 1547

EP - 1583

JO - Applied Mathematics & Optimization

JF - Applied Mathematics & Optimization

IS - 3

ER -

Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this