Uma versão abstrata do princípio de concentração de compacidade e aplicações

Abstract

In this work we present an abstract version of the concentration compactness principle by Lions, extending it to Hilbert spaces. To do so, we include the concept of dislocation space, the pair (H;D) formed by a separable Hilbert space H (being H1(RN) the model case, N 3) and a set D of linear limited operators on H; as well as the concept of the D-weak convergence. The main result of this theory is, in a sense, a generalization of the famous theorem of Banach-Bourbaki-Alaoglu. Another important consequence of the theory is the equivalence of D-weak convergence in H1(RN);N 3 and strong convergence in Lp; for p 2 (2; 2 ) and D appropriate. With this version, we prove existence of solution for some classes of elliptic problem on unbounded domains, via constrained minimization method.