The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions

Hongjie Dong; Zongyuan Li

doi:10.1080/03605302.2020.1845204

The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions

Hongjie Dong^*
, Zongyuan Li

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We consider the mixed Dirichlet-conormal problem on irregular domains in R^d: Two types of regularity results will be discussed: the W^1,^p regularity and a non-tangential maximal function estimate. The domain is assumed to be Reifenberg-flat, and the interfacial boundary is either Reifenberg-flat of co-dimension 2 or is locally sufficiently close to a Lipschitz function of m variables, where m = 1, ..., d − 2. For the non-tangential maximal function estimate, we also require the domain to be Lipschitz. © 2020 Taylor & Francis Group, LLC.

Original language	English
Pages (from-to)	470-497
Journal	Communications in Partial Differential Equations
Volume	46
Issue number	3
Online published	16 Nov 2020
DOIs	https://doi.org/10.1080/03605302.2020.1845204
Publication status	Published - 2021
Externally published	Yes

Research Keywords

Inhomogeneous boundary conditions
mixed Dirichletconormal boundary value problem
nontangential maximal function estimates
Reifenberg flat domains and separations
VMO coefficients
W{1,p} estimates and solvability

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title = "The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions",

abstract = "We consider the mixed Dirichlet-conormal problem on irregular domains in Rd: Two types of regularity results will be discussed: the W1,p regularity and a non-tangential maximal function estimate. The domain is assumed to be Reifenberg-flat, and the interfacial boundary is either Reifenberg-flat of co-dimension 2 or is locally sufficiently close to a Lipschitz function of m variables, where m = 1, ..., d − 2. For the non-tangential maximal function estimate, we also require the domain to be Lipschitz. {\textcopyright} 2020 Taylor \& Francis Group, LLC.",

keywords = "Inhomogeneous boundary conditions, mixed Dirichletconormal boundary value problem, nontangential maximal function estimates, Reifenberg flat domains and separations, VMO coefficients, W\{1,p\} estimates and solvability",

author = "Hongjie Dong and Zongyuan Li",

year = "2021",

doi = "10.1080/03605302.2020.1845204",

language = "English",

volume = "46",

pages = "470--497",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor \& Francis",

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TY - JOUR

T1 - The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions

AU - Dong, Hongjie

AU - Li, Zongyuan

PY - 2021

Y1 - 2021

N2 - We consider the mixed Dirichlet-conormal problem on irregular domains in Rd: Two types of regularity results will be discussed: the W1,p regularity and a non-tangential maximal function estimate. The domain is assumed to be Reifenberg-flat, and the interfacial boundary is either Reifenberg-flat of co-dimension 2 or is locally sufficiently close to a Lipschitz function of m variables, where m = 1, ..., d − 2. For the non-tangential maximal function estimate, we also require the domain to be Lipschitz. © 2020 Taylor & Francis Group, LLC.

AB - We consider the mixed Dirichlet-conormal problem on irregular domains in Rd: Two types of regularity results will be discussed: the W1,p regularity and a non-tangential maximal function estimate. The domain is assumed to be Reifenberg-flat, and the interfacial boundary is either Reifenberg-flat of co-dimension 2 or is locally sufficiently close to a Lipschitz function of m variables, where m = 1, ..., d − 2. For the non-tangential maximal function estimate, we also require the domain to be Lipschitz. © 2020 Taylor & Francis Group, LLC.

KW - Inhomogeneous boundary conditions

KW - mixed Dirichletconormal boundary value problem

KW - nontangential maximal function estimates

KW - Reifenberg flat domains and separations

KW - VMO coefficients

KW - W{1,p} estimates and solvability

UR - https://www.scopus.com/pages/publications/85096147675

UR - https://www.scopus.com/pages/publications/85096147675#tab=impact

U2 - 10.1080/03605302.2020.1845204

DO - 10.1080/03605302.2020.1845204

M3 - RGC 21 - Publication in refereed journal

SN - 0360-5302

VL - 46

SP - 470

EP - 497

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 3

ER -

The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions

Abstract

Research Keywords

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