Some classes of Sobolev spaces
Patrizia Donato · 1999
Abstract In this chapter we introduce the functional setting, essentially based on the distribution theory and Sobolev spaces, which is the natural framework for the homogenization results we present in this book. Distributions and Sobolev spaces have been widely studied in the last fifty years. We refer the reader for instance to Schwartz (1951), Nečas (1967), Lions and Magenes (1968a,b), Adams (1975), and Mazya (1985). We will quote here just the main results which will be used later. We also present, in the same context, some specific spaces of periodic functions as well as their main properties.