Fractional order Orlicz-Sobolev spaces

被引：112
|
作者：
Fernandez Bonder, Julian [1 ]
Salort, Ariel M. [1 ,2 ]
机构：
[1] Univ Buenos Aires, FCEyN, Dept Matemat, Ciudad Univ,Pabellon 1,Ave Cantilo S-N, RA-1428 Buenos Aires, DF, Argentina
[2] Consejo Nacl Invest Cient & Tecn, IMAS, Ciudad Univ,Pabellon 1,Ave Cantilo S-N, RA-1428 Buenos Aires, DF, Argentina
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 277卷 / 02期
关键词：
Fractional order Sobolev spaces; Orlicz-Sobolev spaces; g-Laplace operator; LEVY; EQUATIONS; BOUNDARY; PATTERNS; BOURGAIN; BREZIS;
D O I：
10.1016/j.jfa.2019.04.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we define the fractional order Orlicz-Sobolev spaces, and prove its convergence to the classical OrliczSobolev spaces when the fractional parameter s up arrow 1 in the spirit of the celebrated result of Bourgain-Brezis-Mironescu. We then deduce some consequences such as Gamma-convergence of the modulars and convergence of solutions for some fractional versions of the Delta(g) operator as the fractional parameter s up arrow 1. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：333 / 367
页数：35
相关论文
共 50 条
  • [21] Removable Sets for Orlicz-Sobolev Spaces
    Karak, Nijjwal
    POTENTIAL ANALYSIS, 2015, 43 (04) : 675 - 694
  • [22] DISTANCE FUNCTIONS AND ORLICZ-SOBOLEV SPACES
    EDMUNDS, DE
    EDMUNDS, RM
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1986, 38 (05): : 1181 - 1198
  • [23] Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces
    Bahrouni, Sabri
    Salort, Ariel M.
    ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2021, 27
  • [24] Ground State Solutions for a Nonlocal System in Fractional Orlicz-Sobolev Spaces
    El-Houari, Hamza
    Moussa, Hicham
    Chadli, Lalla Saadia
    INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 2022
  • [25] Extension in generalized Orlicz-Sobolev spaces
    Juusti, Jonne
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 522 (01)
  • [26] AN EXTENSION OPERATOR FOR ORLICZ-SOBOLEV SPACES
    DESOUZA, AJ
    ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 1981, 53 (01): : 9 - 12
  • [27] Composition operators in Orlicz-Sobolev spaces
    Menovshchikov, A. V.
    SIBERIAN MATHEMATICAL JOURNAL, 2016, 57 (05) : 849 - 859
  • [28] Interpolation operators in Orlicz-Sobolev spaces
    Diening, L.
    Ruzicka, M.
    NUMERISCHE MATHEMATIK, 2007, 107 (01) : 107 - 129
  • [29] A Harnack inequality in Orlicz-Sobolev spaces
    Arriagad, Waldo
    Huentutripay, Jorge
    STUDIA MATHEMATICA, 2018, 243 (02) : 117 - 137
  • [30] MULTIPLE SOLUTIONS FOR A NONLOCAL KIRCHHOFF PROBLEM IN FRACTIONAL ORLICZ-SOBOLEV SPACES
    Azroul, Elhoussine
    Benkirane, Abdelmoujib
    Srati, Mohammed
    Xiang, Mingqi
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2025, 49 (02): : 287 - 303
12345