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

Sergio Conti, Georg Dolzmann, Stefan Müller

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 t…