Microscopic structures from reduction of continuum nonlinear problems
DOI:
https://doi.org/10.1478/AAPP.91S1A4Abstract
We present an application of the Amann–Zehnder exact finite reduction to a class of nonlinear perturbations of elliptic elasto-static problems. We propose the existence of minmax solutions by applying Ljusternik–Schnirelmann theory to a finite dimensional variational formulation of the problem, based on a suitable spectral cut–off. As a by–product, 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.
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Published
2013-01-29
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Special issue in memory of Prof. Giovanni Crupi
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