Regularity results of the thin obstacle problem for the p(x)-Laplacian

Sun Sig Byun; Ki Ahm Lee; Jehan Oh; Jinwan Park

doi:10.1016/j.jfa.2018.06.003

Regularity results of the thin obstacle problem for the p(x)-Laplacian

Sun Sig Byun, Ki Ahm Lee, Jehan Oh, Jinwan Park

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

10 Scopus citations

Abstract

We study thin obstacle problems involving the energy functional with p(x)-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent p(x) is Hölder continuous.

Original language	English
Pages (from-to)	496-519
Number of pages	24
Journal	Journal of Functional Analysis
Volume	276
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2018.06.003
State	Published - 15 Jan 2019

Keywords

Regularity
Thin obstacle problem
Variable exponent
p(x)-Laplacian

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10.1016/j.jfa.2018.06.003

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title = "Regularity results of the thin obstacle problem for the p(x)-Laplacian",

abstract = "We study thin obstacle problems involving the energy functional with p(x)-growth. We prove higher integrability and H{\"o}lder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent p(x) is H{\"o}lder continuous.",

keywords = "Regularity, Thin obstacle problem, Variable exponent, p(x)-Laplacian",

author = "Byun, {Sun Sig} and Lee, {Ki Ahm} and Jehan Oh and Jinwan Park",

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

year = "2019",

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T1 - Regularity results of the thin obstacle problem for the p(x)-Laplacian

AU - Byun, Sun Sig

AU - Lee, Ki Ahm

AU - Oh, Jehan

AU - Park, Jinwan

PY - 2019/1/15

Y1 - 2019/1/15

N2 - We study thin obstacle problems involving the energy functional with p(x)-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent p(x) is Hölder continuous.

AB - We study thin obstacle problems involving the energy functional with p(x)-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent p(x) is Hölder continuous.

KW - Regularity

KW - Thin obstacle problem

KW - Variable exponent

KW - p(x)-Laplacian

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U2 - 10.1016/j.jfa.2018.06.003

DO - 10.1016/j.jfa.2018.06.003

M3 - Article

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SN - 0022-1236

VL - 276

SP - 496

EP - 519

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Regularity results of the thin obstacle problem for the p(x)-Laplacian

Abstract

Keywords

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