Abstract
In this chapter we shall introduce some function spaces and enucleate certain properties of basic importance for further developments. Particular emphasis will be given to what are called homogeneous Sobolev spaces, which will play a fundamental role in the study of flow in exterior domains. We shall not attempt, however, to give an exhaustive treatment of the subject, since this is beyond the scope of the book. Therefore, the reader who wants more details is referred to the specialised literature quoted throughout. As a rule, we only give proofs where they are elementary or when the result is new or does not seem to be widely known.
Incipe parve puer risu cognoscere matrem.
VERGILIUS, Bucolica IV, v.60
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Galdi, G.P. (1994). Basic Function Spaces and Related Inequalities. In: An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Springer Tracts in Natural Philosophy, vol 38. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3866-7_2
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