| Autor: |
Conti, Sergio, Dolzmann, Georg, Müller, Stefan |
| Rok vydání: |
2009 |
| Předmět: |
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| Zdroj: |
Comptes Rendus Math. 349 (2011), 175-178 |
| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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