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
  • [1] Magnetic fractional order Orlicz-Sobolev spaces
    Fernandez Bonder, Julian
    Salort, Ariel M.
    STUDIA MATHEMATICA, 2021, 259 (01) : 1 - 24
  • [2] On fractional Orlicz-Sobolev spaces
    Alberico, Angela
    Cianchi, Andrea
    Pick, Lubos
    Slavikova, Lenka
    ANALYSIS AND MATHEMATICAL PHYSICS, 2021, 11 (02)
  • [3] HARDY INEQUALITIES IN FRACTIONAL ORLICZ-SOBOLEV SPACES
    Salort, Ariel M.
    PUBLICACIONS MATEMATIQUES, 2022, 66 (01) : 183 - 195
  • [4] EMBEDDING THEOREMS ON THE FRACTIONAL ORLICZ-SOBOLEV SPACES
    Jung, Tacksun
    Choi, Q-Heung
    KOREAN JOURNAL OF MATHEMATICS, 2021, 29 (01): : 56 - 63
  • [5] Boundedness of functions in fractional Orlicz-Sobolev spaces
    Alberico, Angela
    Cianchi, Andrea
    Pick, Lubos
    Slavikova, Lenka
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2023, 230
  • [6] Some embedding theorems on the variable-order fractional Orlicz-Sobolev spaces
    Choi, Q-Heung
    Jung, Tacksun
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024,
  • [7] Hardy and Poincare inequalities in fractional Orlicz-Sobolev spaces
    Bal, Kaushik
    Mohanta, Kaushik
    Roy, Prosenjit
    Sk, Firoj
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 216
  • [8] A class of elliptic inclusion in fractional Orlicz-Sobolev spaces
    El-houari, Hamza
    Moussa, Hicham
    Chadli, Lalla Saadia
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024, 69 (05) : 755 - 772
  • [9] On a class of nonvariational problems in fractional Orlicz-Sobolev spaces
    Bahrouni, Anouar
    Bahrouni, Sabri
    Xiang, Mingqi
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 190
  • [10] ON THE FRACTIONAL ELLIPTIC PROBLEMS WITH DIFFERENCE IN THE ORLICZ-SOBOLEV SPACES
    Jung, Tacksun
    Choi, Q-Heung
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2022, 27 (5-6) : 385 - 406
12345