THE DIRICHLET PROBLEM FOR NONLOCAL LEVY-TYPE OPERATORS

被引：9
|
作者：
Rutkowski, Artur [1 ]
机构：
[1] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wybrzeze Wyspianskiego 27, PL-50370 Wroclaw, Poland
来源：
PUBLICACIONS MATEMATIQUES | 2018年 / 62卷 / 01期
关键词：
Dirichlet problem; nonlocal operator; maximum principle; weak solutions; extension operator; EQUATIONS; DOMAINS;
D O I：
10.5565/PUBLMAT6211811
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present the theory of the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric Levy processes whose Levy measures need not be absolutely continuous. We establish basic facts about the Sobolev spaces for such operators, in particular we prove the existence and uniqueness of weak solutions. We present strong and weak variants of maximum principle, and bounds for solutions. We also discuss the related extension problem in C-1,C-1 domains.
引用
收藏
页码：213 / 251
页数：39
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