arXiv 0712.21332007-12-13math.FAmath.AP

再论Div-Curl引理

The Div-Curl Lemma Revisited

Dan Polisevski

摘要：

Div-Curl引理是索伯列夫空间中补偿紧性理论的基本结果，由F. Murat（1978）给出了$L^2(Ω)$和$L^p(Ω)$，$p \neq 2$情形的不同证明。在本文中，我们提出了一个略有不同的证明，只依赖于格林-高斯积分公式和通常的Rellich-Kondrachov紧性。

英文摘要：

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 $L^2(Ω)$ and $L^p(Ω)$, $p \neq 2$, 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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