Download An Introduction to Homogenization by Doina Cioranescu, Patrizia Donato PDF

f in D'(0). 11 (derivative of a distribution). Let T E D'(0). For ally i = 1, ... 12. It is easy to check that OT/8xi. i = 1....

11). 9), it is easily seen that [N(s) + N'(`)JeN < Ciyl[ . 16) for a small enough. 0 3 Some classes of Sobolev spaces 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), Nebas (1967), Lions and Magenes (1968a,b), Adams (1975), and Mazya (1985).

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