Fractional elliptic problem in exterior domains with nonlocal Neumann condition. (June 2020) - Alves, Claudianor O.; Torres Ledesma, César E.
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 .