Function spaces and extension results for nonlocal Dirichlet problems

被引：19

作者：

Dyda, Bartlomiej ^{[1
]}

Kassmann, Moritz ^{[2
]}

机构：

[1] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wybrzeze Wyspianskiego 27, PL-50370 Wroclaw, Poland

[2] Univ Bielefeld, Fak Math, Postfach 100131, D-33501 Bielefeld, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 277卷 / 11期

关键词：

Nonlocal Dirichlet problem; Trace theorem; Extension operator; Integrodifferential equation;

D O I：

10.1016/j.jfa.2018.10.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study function spaces and extension results in relation with Dirichlet problems involving integrodifferential operators. For such problems, data are prescribed on the complement of a given domain Omega subset of R-d. We introduce a function space that serves as a trace space for nonlocal Dirichlet problems and study related extension results. (C) 2018 Published by Elsevier Inc.

引用

页数：22

共 13 条

[1]

Adams Robert A., 2003, Pure Appl. Math. (Amst.), V140

[2]

[Anonymous], 1970, SINGULAR INTEGRALS D

[3]

Bourgain J, 2001, OPTIMAL CONTROL AND PARTIAL DIFFERENTIAL EQUATIONS, P439

[4] Nonlocal problems with Neumann boundary conditions [J].