Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations

Yuzhou Fang; Bin Shang; Chao Zhang

doi:10.1007/s12220-021-00768-0

Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations

Yuzhou Fang
, Bin Shang
, Chao Zhang^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

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

25 Scopus citations

Abstract

We investigate the mixed local and nonlocal parabolic p-Laplace equation ∂tu(x,t)-Δpu(x,t)+Lu(x,t)=0,where Δ _p is the usual local p-Laplace operator and L is the nonlocal p-Laplace type operator. Based on the combination of suitable Caccioppoli-type inequality and Logarithmic Lemma with a De Giorgi–Nash–Moser iteration, we establish the local boundedness and Hölder continuity of weak solutions for such equations.

Original language	English
Article number	22
Journal	Journal of Geometric Analysis
Volume	32
Issue number	1
DOIs	https://doi.org/10.1007/s12220-021-00768-0
State	Published - Jan 2022
Externally published	Yes

Keywords

Hölder continuity
Local boundedness
Mixed local and nonlocal parabolic p-Laplace equation

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10.1007/s12220-021-00768-0

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title = "Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations",

abstract = "We investigate the mixed local and nonlocal parabolic p-Laplace equation ∂tu(x,t)-Δpu(x,t)+Lu(x,t)=0,where Δ p is the usual local p-Laplace operator and L is the nonlocal p-Laplace type operator. Based on the combination of suitable Caccioppoli-type inequality and Logarithmic Lemma with a De Giorgi–Nash–Moser iteration, we establish the local boundedness and H{\"o}lder continuity of weak solutions for such equations.",

keywords = "H{\"o}lder continuity, Local boundedness, Mixed local and nonlocal parabolic p-Laplace equation",

author = "Yuzhou Fang and Bin Shang and Chao Zhang",

note = "Publisher Copyright: {\textcopyright} 2021, Mathematica Josephina, Inc.",

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T1 - Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations

AU - Fang, Yuzhou

AU - Shang, Bin

AU - Zhang, Chao

PY - 2022/1

Y1 - 2022/1

N2 - We investigate the mixed local and nonlocal parabolic p-Laplace equation ∂tu(x,t)-Δpu(x,t)+Lu(x,t)=0,where Δ p is the usual local p-Laplace operator and L is the nonlocal p-Laplace type operator. Based on the combination of suitable Caccioppoli-type inequality and Logarithmic Lemma with a De Giorgi–Nash–Moser iteration, we establish the local boundedness and Hölder continuity of weak solutions for such equations.

AB - We investigate the mixed local and nonlocal parabolic p-Laplace equation ∂tu(x,t)-Δpu(x,t)+Lu(x,t)=0,where Δ p is the usual local p-Laplace operator and L is the nonlocal p-Laplace type operator. Based on the combination of suitable Caccioppoli-type inequality and Logarithmic Lemma with a De Giorgi–Nash–Moser iteration, we establish the local boundedness and Hölder continuity of weak solutions for such equations.

KW - Hölder continuity

KW - Local boundedness

KW - Mixed local and nonlocal parabolic p-Laplace equation

UR - https://www.scopus.com/pages/publications/85120949439

U2 - 10.1007/s12220-021-00768-0

DO - 10.1007/s12220-021-00768-0

M3 - 文章

AN - SCOPUS:85120949439

SN - 1050-6926

VL - 32

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

M1 - 22

ER -

Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations

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Keywords

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