Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Next Article Journal of Convex Analysis 08 (2001), No. 2, 511--532Copyright Heldermann Verlag 2001 Lavrentieff Phenomenon and Non Standard Growth Conditions Giuseppe Cardone Dip. di Ingegneria Civile, Seconda Università di Napoli, Real Casa dell'Annunziata, Via Roma 29, 81031 Aversa, Italy C. D'Apice Dip. di Ingegneria dell'Informazione e Matematica Applicata, Università di Salerno, Via Ponte don Melillo, 84084 Fisciano, Italy U. De Maio Dip. di Matematica ed Applicazioni, Università di Napoli, Complesso Monte S. Angelo, 80126 Napoli, Italy [Abstract-pdf] The functional $F(u) = \int_B f(x,Du)\,dx$ is considered, where $B$ is the unit ball in $\mathbb{R}^n$, $u$ varies in the set of the locally Lipschitz functions on $\mathbb{R}^n$, and $f$ belongs to a family of integrands containing, as model case, the following one $f:(x,z)\in \mathbb{R}^{n}\times \mathbb{R}^{n}\mapsto \frac{|\lt z,x \lt|}{|x|^{n}}% + |z|^{p},\text{ \ \ \ }1 \lt p \lt n.$ The computation of the relaxed functional of $F$ is provided. The formula obtained shows the persistence of the Lavrentieff Phenomenon. Examples of integrands not exhibiting the Lavrentieff Phenomenon are also presented, showing that this phenomenon is not linked only to the non standard growth behaviour of integrands. [ Fulltext-pdf  (506  KB)]