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
相关论文
共 32 条
  • [1] Andreu F., 2010, Mathematical Surveys and Monographs American Mathematical Society, V165
  • [2] CAN THE NONLOCAL CHARACTERIZATION OF SOBOLEV SPACES BY BOURGAIN ET AL. BE USEFUL FOR SOLVING VARIATIONAL PROBLEMS?
    Aubert, Gilles
    Kornprobst, Pierre
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (02) : 844 - 860
  • [3] Symmetric jump processes: Localization, heat kernels and convergence
    Bass, Richard F.
    Kassmann, Moritz
    Kumagai, Takashi
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2010, 46 (01): : 59 - 71
  • [4] Borghol R, 2007, ASYMPTOTIC ANAL, V51, P303
  • [5] Bourgain J, 2001, OPTIMAL CONTROL AND PARTIAL DIFFERENTIAL EQUATIONS, P439
  • [6] Image Denoising Methods. A New Nonlocal Principle
    Buades, A.
    Coll, B.
    Morel, J. M.
    [J]. SIAM REVIEW, 2010, 52 (01) : 113 - 147
  • [7] CLASSICAL, NONLOCAL, AND FRACTIONAL DIFFUSION EQUATIONS ON BOUNDED DOMAINS
    Burch, Nathanial
    Lehoucq, R. B.
    [J]. INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, 2011, 9 (06) : 661 - 674
  • [8] An extension problem related to the fractional Laplacian
    Caffarelli, Luis
    Silvestre, Luis
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1245 - 1260
  • [9] Hitchhiker's guide to the fractional Sobolev spaces
    Di Nezza, Eleonora
    Palatucci, Giampiero
    Valdinoci, Enrico
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (05): : 521 - 573
  • [10] A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
    Du, Qiang
    Gunzburger, Max
    Lehoucq, R. B.
    Zhou, Kun
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2013, 23 (03) : 493 - 540
1234