A critical elliptic problem involving fractional Laplacian operator in domains with shrinking holes

Abstract Let Ω e be a bounded domain in R N with small holes. In this paper, we study the existence of solutions for the following problem { ( − Δ ) s u = u 2 s ⁎ − 1 , u > 0 , in Ω e , u = 0 , in R N ∖ Ω e , where 0 s 1 and 2 s ⁎ = 2 N N − 2 s . We construct solutions which blow up like a volcano near the center of each hole in Ω e