A Class of High Order Nonlocal Operators

被引：7
|
作者：
Tian, Xiaochuan [1 ]
Du, Qiang [1 ]
机构：
[1] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2016年 / 222卷 / 03期
基金：
美国国家科学基金会;
关键词：
ANOMALOUS DIFFUSION; SOBOLEV; NONORDINARY; SPACES; GUIDE;
D O I：
10.1007/s00205-016-1025-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a class of nonlocal operators that may be seen as high order generalizations of the well known nonlocal diffusion operators. We present properties of the associated nonlocal functionals and nonlocal function spaces including nonlocal versions of Sobolev inequalities such as the nonlocal Poincar, and nonlocal Gagliardo-Nirenberg inequalities. Nonlocal characterizations of high order Sobolev spaces in the spirit of Bourgain-Brezis-Mironescu are provided. Applications of nonlocal calculus of variations to the well-posedness of linear nonlocal models of elastic beams and plates are also considered.
引用
收藏
页码：1521 / 1553
页数：33
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