Asymptotic analysis of a second-order singular perturbation model for phase transitions

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Cicalese, Marco
Spadaro, Emanuele Nunzio
Zeppieri, Caterina Ida
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Abstract
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We consider the problem of the asymptotic description of a family of energies introduced by Coleman and Mizel in the theory of nonlinear second-order materials depending on an extra parameter k. By proving a new nonlinear interpolation inequality, we show that there exists a positive constant k_0 such that, for k<k_0, these energies Gamma-converge to a sharp interface functional. Moreover, for a special choice of the potential term in the energy, we provide an upper bound on the values of k such that minimizers cannot develop oscillations on some fine scale, thus improving previous estimates by Mizel, Peletier and Troy.
Comment: 19 pages
Keywords
Mathematics - Functional Analysis, 49J45, 49M25, 74B05, 76A15
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