Calculus of Variations and Geometric Measure Theory

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