Boundary blow up solutions for fractional elliptic equations

Abstract

In this talk we discuss existence of boundary blow up solutions for some fractional elliptic equations including (−∆)u+ u = f in Ω, u = g on Ω, lim x∈Ω,x→∂Ω u(x) = ∞, where Ω is a bounded domain of class C2, α ∈ (0, 1) and the functions f : Ω → R and g : RN Ω → R are continuous. We obtain existence and boundary behavior of solution under different hypothesis on f and g. We also prove uniqueness of positive solutions. This work is in collaboration with Huyuan Chen and Alexander Quaas.