Raguž, Andrija:
A Note on Calculation of Asymptotic Energy for a Functional of Ginzburg-Landau Type with Externally Imposed Lower-Order Oscillatory Term in One Dimension
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.3, p. 1125-1142, Unione Matematica Italiana (English)
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Sunto
In questa nota consideriamo il funzionale di Ginzburg-Landau \begin{equation*}I^\epsilon_a(v) = \int_0^1 (\epsilon^2 v''^2(s) + W(v'(s)) + a(\epsilon^{-\beta}s(v^2(s)) \, ds\end{equation*} ove $\beta > 0$ e $a$ è 1-periodica. Mostreremo come la minima energia asintotica (ridimensionata) associata a $I^\epsilon_a$ dipenda dal parametro $\beta > 0$ per $\epsilon \to 0$. In particolare, la nostra analisi mostra che i minimizzatori di $I^\epsilon_a$ sono quasi $\epsilon^{1/3}$-periodici.
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