Calculus of Variations and Geometric Measure Theory
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C. De Lellis

An example in the gradient theory of phase transitions

created on 04 Dec 2001
modified by delellis on 03 May 2011


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


We prove by giving an example that when $n> 2$ the asymptotic behavior of functionals

intOmega eps
\nabla2 u
2 + (1-
\nabla u

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.

For the most updated version and eventual errata see the page


Keywords: phase transitions, $\Gamma$--convergence, ginzburg--landau, singular perturbation

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