THE PARABOLIC HARNACK INEQUALITY FOR NONLOCAL EQUATIONS

被引：0

作者：

Kassmann, Moritz ^{[1
]}

Weidner, Marvin ^{[2
]}

机构：

[1] Univ Bielefeld, Fak Math, Bielefeld, Germany

[2] Univ Barcelona, Dept Matemat & Informat, Barcelona, Spain

来源：

DUKE MATHEMATICAL JOURNAL | 2024年 / 173卷 / 17期

基金：

欧洲研究理事会;

关键词：

NONLINEAR INTEGRODIFFERENTIAL OPERATORS; HEAT KERNELS; REGULARITY THEORY; FORMS;

D O I：

10.1215/00127094-2024-0008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove the parabolic Harnack inequality and H & ouml;lder regularity estimates. We discuss in detail the shortcomings of previous results in this direction. The key element of our approach is a fine study of the nonlocal tail term.

引用

页码：3413 / 3451

页数：39

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