Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations
Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations
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混合局部和非局部抛物型 p-拉普拉斯方程的正则理论
DOI：
10.1007/s12220-021-00768-0
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Chao Zhang
中科院分区：
文献类型：
--
作者：
Yuzhou Fang;Bin Shang;Chao Zhang
We investigate the mixed local and nonlocal parabolic p-Laplace equation ∂tu(x,t)-Δpu(x,t)+Lu(x,t)=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t u(x,t)-\Delta _p u(x,t)+\mathcal {L}u(x,t)=0, \end{aligned}$$\end{document}where Δp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _p$$\end{document} is the usual local p-Laplace operator and L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document} 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.
We investigate the mixed local and nonlocal parabolic p-Laplace equation ∂tu(x,t)-Δpu(x,t)+Lu(x,t)=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t u(x,t)-\Delta _p u(x,t)+\mathcal {L}u(x,t)=0, \end{aligned}$$\end{document}where Δp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _p$$\end{document} is the usual local p-Laplace operator and L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document} 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.
DOI：
10.4171/rmi/609
发表时间：
2008-08
期刊：
arXiv: Probability
影响因子：
--
作者：
Zhen-Qing Chen;T. Kumagai
通讯作者：
Zhen-Qing Chen;T. Kumagai