ABSTRACT

We shall prove that the set Oc,r(B ) is compact in the iP-topology, and because of the continuity of the shape functionals which are defined on the solutions we will obtain some existence results.

T heorem 5.1. The family 0 Cyr(B) defined in the definition 4-2. is compact. Proof: It is sufficient to prove that:

Vc > 0, Vr, 0 < r < 1 clHcOc,r{B) = Oc,r(B)