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An example in the gradient theory of phase transitions
Published online by Cambridge University Press: 15 September 2002
Abstract
We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals $\int_\Omega \varepsilon|\nabla^2 u|^2+(1-|\nabla u|^2)^2/\varepsilon$ is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
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- © EDP Sciences, SMAI, 2002
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