Lower semicontinuity of quasiconvex integrals. (English) Zbl 0862.49017

Summary: New lower semicontinuity results for quasiconvex integrals are established. In particular, under certain structure conditions and growth \(0\leq F(\xi)\leq C(1+|\xi|^q)\) the functional \(\int_{\Omega}F(\nabla u)dx\) is proved to be lower semicontinuous on \(W^{1,q}\) with respect to the weak convergence in \(W^{1,p}\), \(p\geq q-1\).


49J45 Methods involving semicontinuity and convergence; relaxation
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