Extension and trace for nonlocal operators

被引：30

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.

引用

页码：33 / 69

页数：37

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