A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional p(⋅)-Laplacian. (November 2019)

• Record Type: Journal Article
• Authors: Ho, Ky; Kim, Yun-Ho
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 179
• Page End: 201
• Publication Date: 2019-11
• Subjects: 35B45 -- 35D30 -- 35J20 -- 35J60 -- 35J92 -- 35R11 -- 46E35; Fractional p-Laplacian -- p(⋅)-Laplacian -- Fractional Sobolev spaces with variable exponents -- A-priori bounds -- De Giorgi iteration -- Variational methods; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.06.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.