Local properties for weak solutions of nonlocal heat equations

被引：7
|
作者：
Kim, Yong-Cheol [1 ,2 ]
机构：
[1] Korea Univ, Dept Math Educ, Seoul 02841, South Korea
[2] Korea Inst Adv Study, Sch Math, Seoul 02455, South Korea
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 192卷
基金：
新加坡国家研究基金会;
关键词：
INEQUALITY; REGULARITY;
D O I：
10.1016/j.na.2019.111689
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, using the De Giorgi-Nash-Moser theory, we obtain an interior parabolic Holder regularity for weak solutions of nonlocal heat equations given by an integro-differential operator L-K as follows; {LKu+partial derivative tu = 0 in Omega x (-T,0] u=g in ((R-n\Omega)x(-T,0])boolean OR(Omega x{t=-T}) where g is an element of C(R(n)x[-T, 0]) boolean AND L-infinity(R(n)x(-T, 0]) boolean AND H-T(s) (R-n) and Omega subset of R-n is a bounded domain with Lipschitz boundary. In addition, we get the local boundedness of such weak solutions. (C) 2019 Elsevier Ltd. All rights reserved.
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页数：30
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