On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma

Abstract

We study connections between four different types of results that are concerned with vector-valued functions u : Ω→ℝ³ of class L²(Ω) on a domain Ω ⊂ ℝ³: Coercivity results in H^1(Ω) relying on div and curl, the Helmholtz decomposition, the construction of vector potentials, and the global div-curl lemma.