Imersões ótimas para espaços de Sobolev reduzidos

Abstract

In this work, we will present the spaces of Orlicz, Zygmund and Lorentz in order to show that certain reduced Sobolev spaces can be optimally immersed in these spaces. The work reviews the classical embeddings of traditional Sobolev spaces in exponential Orlicz spaces (embeddings due to the famous Trudinger-Moser inequality) and ends with generalizations of these embeddings to reduced Sobolev spaces with L1 data.