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W^{-1，1}中散度和旋度均为紧的序列的div-curl引理

The div-curl lemma for sequences whose divergence and curl are compact in W^{-1,1}

Sergio Conti, Georg Dolzmann, Stefan Müller

发表信息：
Comptes Rendus Math. 349 (2011), 175-178
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摘要：

证明了当序列$\Div u_k$和$\curl v_k$在$W^{1,\infty}_0$的对偶空间中是紧的且$u_k\cdot v_k$是等积的时，若$u_k\weakto u$在$L^p$中弱收敛，$v_k\weakly v$在$L^q$中弱收敛，且有$p, q\in (1,\infty)$，$1/p+1/q=1$.主要的一点是，我们只需要等积的标量积$u_k\cdot v_k$，而不是个别的序列。

英文摘要：

It is shown that $u_k \cdot v_k$ converges weakly to $u\cdot v$ if $u_k\weakto u$ weakly in $L^p$ and $v_k\weakly v$ weakly in $L^q$ with $p, q\in (1,\infty)$, $1/p+1/q=1$, under the additional assumptions that the sequences $\Div u_k$ and $\curl v_k$ are compact in the dual space of $W^{1,\infty}_0$ and that $u_k\cdot v_k$ is equi-integrable. The main point is that we only require equi-integrability of the scalar product $u_k\cdot v_k$ and not of the individual sequences.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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