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On asymptotic behavior for 1‐dimensional functional of Ginzburg‐Landau type with internally‐externally created oscillations of minimizers
Author(s) -
Raguz Andrija
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210286
Subject(s) - generalization , regular polygon , class (philosophy) , type (biology) , mathematics , scale (ratio) , zero (linguistics) , mathematical physics , pure mathematics , mathematical analysis , physics , computer science , quantum mechanics , geometry , philosophy , ecology , linguistics , artificial intelligence , biology
In this note we provide a kind of generalization of the well‐known notion of internally (externally, resp.) created oscillations of minimizers of non‐convex integrands in the calculus of variations. As an example, we consider a class of 1‐dimensional Ginzburg‐Landau functionals (the simplest case being considered in the paper G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761–825 (2001)). We describe asymptotic behavior leading to multiple small scale separation as parameter epsilon tends to zero. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)