An example in the gradient theory of phase transitions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002) , pp. 285-289.

We prove by giving an example that when n3 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 : https://doi.org/10.1051/cocv:2002012
Classification : 49J45,  74G65,  76M30
Mots clés : phase transitions, Γ-convergence, asymptotic analysis, singular perturbation, Ginzburg-Landau
@article{COCV_2002__7__285_0,
     author = {de Lellis, Camillo},
     title = {An example in the gradient theory of phase transitions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {285--289},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2002},
     doi = {10.1051/cocv:2002012},
     zbl = {1037.49010},
     mrnumber = {1925030},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2002012/}
}
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. http://www.numdam.org/articles/10.1051/cocv:2002012/

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