ON A NEW FRACTIONAL SOBOLEV SPACE AND APPLICATIONS TO NONLOCAL VARIATIONAL PROBLEMS WITH VARIABLE EXPONENT

被引：153
|
作者：
Bahrouni, Anouar [1 ]
Radulescu, Vicentiu D. [2 ,3 ]
机构：
[1] Univ Monastir, Math Dept, Fac Sci, Monastir 5019, Tunisia
[2] King Abdulaziz Univ, Dept Math, Fac Sci, POB 80203, Jeddah 21589, Saudi Arabia
[3] Univ Craiova, Dept Math, St AI Cuza 13, Craiova 200585, Romania
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2018年 / 11卷 / 03期
关键词：
Fractional p(x)-Laplace operator; density; integral functional; Gagliardo seminorm; variational method; REGULARITY; EXISTENCE;
D O I：
10.3934/dcdss.2018021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The content of this paper is at the interplay between function spaces L-p(x) and W-k,W-p(x) with variable exponents and fractional Sobolev spaces W-s,W-p. We are concerned with some qualitative properties of the fractional Sobolev space W-s,W-q(x),W-p(x,W-y), where q and p are variable exponents and s is an element of (0, 1). We also study a related nonlocal operator, which is a fractional version of the nonhomogeneous p(x)-Laplace operator. The abstract results established in this paper are applied in the variational analysis of a class of nonlocal fractional problems with several variable exponents.
引用
收藏
页码：379 / 389
页数：11
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