Abstract
Abstract This chapter deals with several auxiliary results of functional analysis which will be broadly used especially in Chapters 4 and 7. In Section 3.1 we prove Friedrich’s lemma about commutators and investigate the renormalized solutions to the steady continuity equation. Section 3.2 is devoted to spaces of vector fields with summable divergence. In Section 3.3 we investigate the equation div v = f in various domains with compact or noncompact boundaries. In Section 3.4 we recall some useful results from the theory of monotone operators and from convex analysis.
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