Global Calderón-Zygmund theory for nonlinear elliptic obstacle problems with asymptotically regular nonlinearities

Sun Sig Byun; Yumi Cho; Jehan Oh

doi:10.1016/j.na.2015.05.003

Global Calderón-Zygmund theory for nonlinear elliptic obstacle problems with asymptotically regular nonlinearities

Sun Sig Byun, Yumi Cho, Jehan Oh

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

9 Scopus citations

Abstract

We study a nonlinear elliptic problem with an irregular obstacle in a bounded nonsmooth domain when the nonlinearity is merely asymptotically regular. We find an optimal regularity requirement on the associated nonlinearity and a minimal geometric condition on the boundary to ensure a global Calderón-Zygmund estimate for such an asymptotically regular obstacle problem. We assume that the associated nonlinearity has a small BMO and the boundary is sufficiently flat in the Reifenberg sense.

Original language	English
Pages (from-to)	150-157
Number of pages	8
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	123-124
DOIs	https://doi.org/10.1016/j.na.2015.05.003
State	Published - 1 Jun 2015

Keywords

Asymptotically regular
BMO
Calderón-Zygmund estimates
Discontinuous nonlinearity
Obstacle problem
Reifenberg domain

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10.1016/j.na.2015.05.003

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abstract = "We study a nonlinear elliptic problem with an irregular obstacle in a bounded nonsmooth domain when the nonlinearity is merely asymptotically regular. We find an optimal regularity requirement on the associated nonlinearity and a minimal geometric condition on the boundary to ensure a global Calder{\'o}n-Zygmund estimate for such an asymptotically regular obstacle problem. We assume that the associated nonlinearity has a small BMO and the boundary is sufficiently flat in the Reifenberg sense.",

keywords = "Asymptotically regular, BMO, Calder{\'o}n-Zygmund estimates, Discontinuous nonlinearity, Obstacle problem, Reifenberg domain",

author = "Byun, {Sun Sig} and Yumi Cho and Jehan Oh",

year = "2015",

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doi = "10.1016/j.na.2015.05.003",

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T1 - Global Calderón-Zygmund theory for nonlinear elliptic obstacle problems with asymptotically regular nonlinearities

AU - Byun, Sun Sig

AU - Cho, Yumi

AU - Oh, Jehan

PY - 2015/6/1

Y1 - 2015/6/1

N2 - We study a nonlinear elliptic problem with an irregular obstacle in a bounded nonsmooth domain when the nonlinearity is merely asymptotically regular. We find an optimal regularity requirement on the associated nonlinearity and a minimal geometric condition on the boundary to ensure a global Calderón-Zygmund estimate for such an asymptotically regular obstacle problem. We assume that the associated nonlinearity has a small BMO and the boundary is sufficiently flat in the Reifenberg sense.

AB - We study a nonlinear elliptic problem with an irregular obstacle in a bounded nonsmooth domain when the nonlinearity is merely asymptotically regular. We find an optimal regularity requirement on the associated nonlinearity and a minimal geometric condition on the boundary to ensure a global Calderón-Zygmund estimate for such an asymptotically regular obstacle problem. We assume that the associated nonlinearity has a small BMO and the boundary is sufficiently flat in the Reifenberg sense.

KW - Asymptotically regular

KW - BMO

KW - Calderón-Zygmund estimates

KW - Discontinuous nonlinearity

KW - Obstacle problem

KW - Reifenberg domain

UR - http://www.scopus.com/inward/record.url?scp=84930680633&partnerID=8YFLogxK

U2 - 10.1016/j.na.2015.05.003

DO - 10.1016/j.na.2015.05.003

M3 - Article

AN - SCOPUS:84930680633

SN - 0362-546X

VL - 123-124

SP - 150

EP - 157

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

Global Calderón-Zygmund theory for nonlinear elliptic obstacle problems with asymptotically regular nonlinearities

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Keywords

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