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MiS Preprint

An example in the gradient theory of phase transitions

Camillo De Lellis


We prove by giving an example that when $n\geq 3$ the asymptotic behavior of functionals $\int_\Omega \epsilon |\nabla^2 u|^2+(1-|\nabla u|^2)^2/\epsilon$ 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 is no longer true in higher dimensions.

MSC Codes:
49J45, 74G65, 76M30
phase transitions, gamma-convergence, asymptotic analysis, singular perturbations, ginzburg--landau

Related publications

2002 Repository Open Access
Camillo De Lellis

An example in the gradient theory of phase transitions

In: Control, optimisation and calculus of variations (ESAIM-COCV), 7 (2002), 285-289 (electronic)