Published Paper
Inserted: 25 sep 2002
Last Updated: 10 jan 2005
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
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
$$
1C(
v
{p}-1)<= f(v)<= C(1+
v
{q})
$$
with $q$ in $( p,pN/(N-1))$ for $p<=N-1$, while $q$ in $( p,p+1)$ for
$p>N-1.$ In particular, our results generalize earlier work where
$A v=0$ reduced to $v=D^{s}u$ for some integer $s$.
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