Fractional elliptic problem in exterior domains with nonlocal Neumann condition. (June 2020)

• Record Type: Journal Article
• Authors: Alves, Claudianor O.; Torres Ledesma, César E.
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: primary 35A15 -- secondary 35J60 35C15; Variational methods -- Nonlinear elliptic equations -- Integral representations of solutions; 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.2019.111732
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the existence of solution for the following class of fractional elliptic problem (0.1) ( − Δ ) s u + u = Q ( x ) | u | p − 1 u in R N ∖ Ω N s u ( x ) = 0 in Ω, where s ∈ ( 0, 1 ), N > 2 s, Ω ⊂ R N is a bounded set with smooth boundary, ( − Δ ) s denotes the fractional Laplacian operator and N s is the nonlocal operator that describes the Neumann boundary condition, which is given by N s u ( x ) = C N, s ∫ R N ∖ Ω u ( x ) − u ( y ) | x − y | N + 2 s d y, x ∈ Ω .