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.
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页码：333 / 367
页数：35
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