*Published Paper*

**Inserted:** 25 sep 2002

**Last Updated:** 10 jan 2005

**Journal:** Ann. Inst. H. PoincarĂ© Anal. Non LinĂ©aire

**Volume:** 21

**Number:** 2

**Pages:** 209-236

**Year:** 2004

**Abstract:**

Lower semicontinuity results with respect to weak-$\ast$ convergence in the
sense of measures and with respect to weak convergence in $L^p$ are
obtained for functionals
$$
F(v)=int_{{Omega}f}(x,v(x))\,dx,
$$
where admissible sequences $\{v_{n}\}$ satisfy a first order system of PDEs
$A v_{n}=0$. We suppose that $A$ has constant rank, $f$ is
$A$-quasiconvex and satisfies the non standard growth conditions
$$
1*C(v*

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