%0 Journal Article
%T Microscopic structures from reduction of continuum nonlinear problems
%A Franco Cardin
%A Alberto Lovison
%J Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali
%D 2013
%I Accademia Peloritana dei Pericolanti
%R 10.1478/aapp.91s1a4
%X We present an application of the Amann¨CZehnder exact finite reduction to a class of nonlinear perturbations of elliptic elasto-static problems. We propose the existence of minmax solutions by applying Ljusternik¨CSchnirelmann theory to a finite dimensional variational formulation of the problem, based on a suitable spectral cut¨Coff. As a by¨Cproduct, with a choice of fit variables, we establish a variational equivalence between the above spectral finite description and a discrete mechanical model. By doing so, we decrypt the abstract information encoded in the AZ reduction and give rise to a concrete and finite description of the continuous problem.
%U http://dx.doi.org/10.1478/AAPP.91S1A4