The Div-Curl Lemma Revisited

Details The Div-Curl Lemma Revisited The Div-Curl Lemma Revisited

2007-12-13

arxiv.org/abs/0712.2133v1

Mathematics

Functional Analysis

Scientific paper

The Div-Curl Lemma, which is the basic result of the compensated compactness
theory in Sobolev spaces, was introduced by F. Murat (1978) with distinct
proofs for the $L^2(\Omega)$ and $L^p(\Omega)$, $p \neq 2$, cases. In this note
we present a slightly different proof, relying only on a Green-Gauss integral
formula and on the usual Rellich-Kondrachov compactness properties.

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