NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS WITH GENERAL STABLE OPERATORS IN WEIGHTED SOBOLEV SPACES*

被引：1

作者：

Dong, Hongjie ^{[1
]}

Ryu, Junhee ^{[2
]}

机构：

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Korea Univ, Dept Math, 145 Anam Ro, Seoul 02841, South Korea

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

nonlocal equations; weighted Sobolev spaces; stable operators; DIRICHLET PROBLEM;

D O I：

10.1137/23M160061X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study nonlo cal elliptic and parabolic equations on C 1, \tau open sets in weighted Sobolev spaces, where \tau \in (0, 1). The operators we consider are infinitesimal generators of symmetric stable Le'\vy processes, whose Le'\vy measures are allowed to be very singular. Additionally, for parabolic equations, the measures are assumed to be merely measurable in the time variable.

引用

页码：4623 / 4661

页数：39

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