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

页码：333 / 367

页数：35

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