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

被引：12
|
作者：
Fang, Yuzhou [1 ]
Shang, Bin [1 ]
Zhang, Chao [1 ,2 ]
机构：
[1] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China
[2] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2022年 / 32卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Local boundedness; Holder continuity; Mixed local and nonlocal parabolic p-Laplace equation; HARNACK INEQUALITIES; DIRICHLET FORMS; PRINCIPLE; BEHAVIOR;
D O I：
10.1007/s12220-021-00768-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the mixed local and nonlocal parabolic p-Laplace equation partial derivative(t) u(x, t) - Delta(p) u (x, t) + L u (x, t) = 0, where Delta(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 Holder continuity of weak solutions for such equations.
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页数：33
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