Estabilidade da convergência fraca sob a ação de operadores não lineares

Abstract

This work is a study on the classic lemma of Brezis and Lieb, which is a improvement of Fatou's lemma because it evaluates the gap between the integral of a functional sequence and the integral of its pointwise limit. It is also showed a relation between this result and weak continuity of nonlinear maps between Lebesgue spaces, namely Nemystkii's operators. The final goal is to apply this tool to find sharp constant for a well-known type of variational inequality. Furthermore, it is obtained a compact Sobolev embedding theorem without any regularity condition on the boundary.