ABSTRACT

Throughout this chapter, we consider x0 ∈ RN , N ≥ 1, R > 0, R2 > R1 > 0, BR(x0) := {x ∈ RN : |x− x0| < R},

AR1,R2(x0) := {x ∈ RN : R1 < |x− x0| < R2}, a continuous function a ∈ C[0,∞) such that

a(t) > 0 for all t > 0, (7.1)

a function g ∈ C[0,∞) ∩ C1(0,∞) such that g(0) = 0, g′(u) > 0 for all u > 0, lim

u↑∞ g(u) =∞, (7.2)

and Ω ∈ {BR(x0), AR1,R2(x0)}. (7.3)

Also, we set d(x) := dist(x, ∂Ω), x ∈ Ω.