Fractional Sobolev spaces with variable exponents and fractional p ( x ) -Laplacians

In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we prove the existence and uniqueness of a solution for a nonlocal problem involving...

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Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2017; no. 76; pp. 1 - 10
Main Authors Kaufmann, Uriel, Rossi, Julio, Vidal, Raul
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2017
Subjects
fractional laplacian
sobolev spaces
variable exponents
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Summary:In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we prove the existence and uniqueness of a solution for a nonlocal problem involving the fractional $p(x)$-Laplacian.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2017.1.76