Abstract
We study minimizers of the singularly perturbed functional I ε(u) = f 01 {ε6Ěu Χ2 Χ + (u Χ2 − 1)2 + u 2} dΧ, subject to u(0) = u(1) = 0. For ε = 0 no minimizers exist and we show that for ε > 0, small, the minimizer is nearly periodic with period proportional to ε. Connections with solid-solid phase transitions in crystals are indicated.
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© 1990 Springer-Verlag
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Müller, S. (1990). Minimizing sequences for nonconvex functionals, phase transitions and singular perturbations. In: Kirchgässner, K. (eds) Problems Involving Change of Type. Lecture Notes in Physics, vol 359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52595-5_83
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DOI: https://doi.org/10.1007/3-540-52595-5_83
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