Geodesic
An example in the gradient theory of phase transitions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 285-289
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We prove by giving an example that when n≥3 the asymptotic behavior of functionals ∫ Ω ε|∇ 2 u| 2 +(1-|∇u| 2 ) 2 /ε 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.

DOI : 10.1051/cocv:2002012
Classification : 49J45, 74G65, 76M30
Keywords: phase transitions, $\Gamma $-convergence, asymptotic analysis, singular perturbation, Ginzburg-Landau 
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     title = {An example in the gradient theory of phase transitions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {285--289},
     year = {2002},
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     doi = {10.1051/cocv:2002012},
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     zbl = {1037.49010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002012/}
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Lellis, Camillo De. An example in the gradient theory of phase transitions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 285-289. doi: 10.1051/cocv:2002012

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