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

Authors: Hồ Ngọc Kỳ (Ky Ho), Kim Yun-Ho,

https://doi.org/10.1016/j.na.2019.06.001

Publisher, magazine: ,

Publication year: 2019

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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 -Laplacian.

Tags: Fractional -Laplacian-Laplacian, Fractional Sobolev spaces with variable exponents, A-priori bounds, De Giorgi iteration, Variational methods