Gradient estimates for double phase problems with irregular obstacles

Sun Sig Byun; Yumi Cho; Jehan Oh

doi:10.1016/j.na.2018.02.008

Gradient estimates for double phase problems with irregular obstacles

Sun Sig Byun
, Yumi Cho
, Jehan Oh

Seoul National University
Korea Institute for Advanced Study

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

14 Scopus citations

Abstract

An irregular obstacle problem with non-uniformly elliptic operator in divergence form of [Formula presented]-growth is studied. We find an optimal regularity for such a double phase obstacle problem by essentially proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence. Calderón–Zygmund type estimates are also obtained under minimal regularity requirements of the prescribed data.

Original language	English
Pages (from-to)	169-185
Number of pages	17
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	177
DOIs	https://doi.org/10.1016/j.na.2018.02.008
State	Published - Dec 2018

Keywords

Calderón–Zygmund estimate
Double phase problem
Obstacle problem

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10.1016/j.na.2018.02.008

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title = "Gradient estimates for double phase problems with irregular obstacles",

abstract = "An irregular obstacle problem with non-uniformly elliptic operator in divergence form of [Formula presented]-growth is studied. We find an optimal regularity for such a double phase obstacle problem by essentially proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence. Calder{\'o}n–Zygmund type estimates are also obtained under minimal regularity requirements of the prescribed data.",

keywords = "Calder{\'o}n–Zygmund estimate, Double phase problem, Obstacle problem",

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

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2018",

month = dec,

doi = "10.1016/j.na.2018.02.008",

language = "English",

volume = "177",

pages = "169--185",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

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T1 - Gradient estimates for double phase problems with irregular obstacles

AU - Byun, Sun Sig

AU - Cho, Yumi

AU - Oh, Jehan

PY - 2018/12

Y1 - 2018/12

N2 - An irregular obstacle problem with non-uniformly elliptic operator in divergence form of [Formula presented]-growth is studied. We find an optimal regularity for such a double phase obstacle problem by essentially proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence. Calderón–Zygmund type estimates are also obtained under minimal regularity requirements of the prescribed data.

AB - An irregular obstacle problem with non-uniformly elliptic operator in divergence form of [Formula presented]-growth is studied. We find an optimal regularity for such a double phase obstacle problem by essentially proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence. Calderón–Zygmund type estimates are also obtained under minimal regularity requirements of the prescribed data.

KW - Calderón–Zygmund estimate

KW - Double phase problem

KW - Obstacle problem

UR - https://www.scopus.com/pages/publications/85042903224

U2 - 10.1016/j.na.2018.02.008

DO - 10.1016/j.na.2018.02.008

M3 - Article

AN - SCOPUS:85042903224

SN - 0362-546X

VL - 177

SP - 169

EP - 185

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

Gradient estimates for double phase problems with irregular obstacles

Abstract

Keywords

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