Microscopic structures from reduction of continuum nonlinear problems
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| Title | Microscopic structures from reduction of continuum nonlinear problems |
| Authors | |
| Abstract | 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. |
| Publisher | Accademia Peloritana dei Pericolanti |
| Date | 2013-01-29 |
| Source | 0365-0359 |
| Rights | Articles and conference papers published in Atti della Accademia Peloritana dei Pericolanti – Classe di Scienze Fisiche, Matematiche e Naturali are distributed under the terms and conditions of a Creative Commons Attribution 3.0 Unported License (effective since 2009, Vol. 87). Correspondingly, authors who publish with this journal agree to the following terms:Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work´s authorship and initial publication in this journal.Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal´s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access). |