A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional p(⋅)-Laplacian

We obtain fundamental imbeddings for fractional Sobolev spaces with variable exponents, which are a generalization of the well-known fractional Sobolev spaces. As an application, we obtain a-priori bounds and multiplicity of solutions to some nonlinear elliptic problems involving the fractional p(⋅)...

Full description

Saved in:
Bibliographic Details
Published inNonlinear analysis Vol. 188; pp. 179 - 201
Main Authors Ho, Ky, Kim, Yun-Ho
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.11.2019
Elsevier BV
Subjects
[formula omitted]-Laplacian
A-priori bounds
De Giorgi iteration
Fractional [formula omitted]-Laplacian
Fractional Sobolev spaces with variable exponents
Imbeddings
Sobolev space
Variational methods
35J20
Variational methods
35J60
35B45
35J92
Fractional p-Laplacian
p(⋅)-Laplacian
46E35
Fractional Sobolev spaces with variable exponents
35D30
35R11
A-priori bounds
De Giorgi iteration
Online AccessGet full text

Cover

More Information
Summary:We obtain fundamental imbeddings for fractional Sobolev spaces with variable exponents, which are a generalization of the well-known fractional Sobolev spaces. As an application, we obtain a-priori bounds and multiplicity of solutions to some nonlinear elliptic problems involving the fractional p(⋅)-Laplacian.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.06.001