Published Paper
Inserted: 4 dec 2001
Last Updated: 3 may 2011
Journal: Control, Optimisation and Calculus of Variations
Volume: 7
Number: 12
Pages: 285-289
Year: 2002
Abstract:
We prove by giving an example that when $n> 2$ the asymptotic behavior of functionals
intOmega eps
\nabla2 u
2 + (1-
\nabla u
2)2eps
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.
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Keywords: phase transitions, $\Gamma$--convergence, ginzburg--landau, singular perturbation