Preliminaries

Abstract

Throughout this book the letters Ω and K always will denote open and compact sets, respectively, in ℝ², and ω will denote a bounded open set with (when necessary) piecewise C¹ boundary ∂ω, which is always supposed to be positively oriented; i.e., one has ω on the left-hand side when passing along ∂ω. The notation ω ⊂⊂ Ω means that the closure of ω is a compact subset of Ω, and d(K,E) denotes the distance between the sets K and E. Moreover, D(a,r) is the open disk with center at a and radius r, and U denotes the unit disk, i.e., U = D(0, 1), and T is its boundary ∂U = {z; ∣;z∣; = 1}. The closure of a set E ∈ ℝ² is denoted by Ē and its interior is denoted by int E.