engleski

On asymptotic behavior for 1-dimensional functional of Ginzburg- Landau type with internally-externally created oscillations of minimizers

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.

Muller's functional, scale separation

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