Comparison and sub-supersolution principles for the fractional p(x)-Laplacian

In this paper we study the new fractional Sobolev space Ws,q(x),p(x,y), where q and p are variable exponents and s∈(0,1), and the related nonlocal operator, which is a fractional version of the nonhomogeneous p(x)-Laplace operator. We first give some further qualitative properties of Ws,q(x),p(x,y)....

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-02, Vol.458 (2), p.1363-1372
Main Author: Bahrouni, Anouar
Format: Article
Language:English
Subjects:
Comparison principle
Fractional [formula omitted]-Laplace operator
Sub-supersolution principle
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Summary:In this paper we study the new fractional Sobolev space Ws,q(x),p(x,y), where q and p are variable exponents and s∈(0,1), and the related nonlocal operator, which is a fractional version of the nonhomogeneous p(x)-Laplace operator. We first give some further qualitative properties of Ws,q(x),p(x,y). We also show the strong comparison principle for the fractional p(x)-Laplace operator. A sub-super-solution for the nonlocal equations involving the fractional p(x)-Laplacian is established.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.10.025