Rellich′s Embedding Theorem for a “Spiny Urchin”

Abstract

From the plane R2 we remove the union of the sets Sk (k = 1, 2, …) defined as follows (using the notation z = x + iy):Sk = {z: arg z = nπ2-k for some integer n; |z|≥k}. The remaining connected open set Ω we call the spiny urchin.