Extension and trace for nonlocal operators

被引：26
|
作者：
Bogdan, Krzysztof [1 ]
Grzywny, Tomasz [1 ]
Pietruska-Paluba, Katarzyna [2 ]
Rutkowski, Artur [1 ]
机构：
[1] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland
[2] Univ Warsaw, Inst Math, Ul Banacha 2, PL-02097 Warsaw, Poland
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2020年 / 137卷
关键词：
Sobolev space; Nonlocal operator; Extension theorem; Harmonic function; DIRICHLET HEAT KERNEL; EQUATIONS; SPACES; DENSITY; THEOREM;
D O I：
10.1016/j.matpur.2019.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem. We give a Douglas-type formula for the quadratic form of the Poisson extension. (C) 2019 Elsevier Masson SAS. All rights reserved.
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页码：33 / 69
页数：37
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