The Solvability of Fractional Elliptic Equation with the Hardy Potential. (28th May 2020) - Gao, Siyu; Huang, Shuibo; Tian, Qiaoyu; Ma, Zhan-Ping
Abstract : In this paper, we study the existence and nonexistence of solutions to fractional elliptic equations with the Hardy potential − Δ s u − λ u / x 2 s = u r − 1 + δ g u, in  Ω, u x > 0, in  Ω, u x = 0, in  ℝ N ∖ Ω, where Ω ⊂ ℝ N is a bounded Lipschitz domain with 0 ∈ Ω, − Δ s is a fractional Laplace operator, s ∈ 0, 1, N > 2 s, δ is a positive number, 2 < r < r λ, s ≡ N + 2 s − 2 α λ / N − 2 s − 2 α λ + 1, α λ ∈ 0, N − 2 s / 2 is a parameter depending on λ, 0 < λ < Λ N, s, and Λ N, s = 2 2 s Γ 2 N + 2 s / 4 / Γ 2 N − 2 s / 4 is the sharp constant of the Hardy–Sobolev inequality.