Second Order Singular Perturbation Models for Phase Transitions

@article{Fonseca2000SecondOS,
  title={Second Order Singular Perturbation Models for Phase Transitions},
  author={Irene Fonseca and Carlo Mantegazza},
  journal={SIAM J. Math. Anal.},
  year={2000},
  volume={31},
  pages={1121-1143}
}
Singular perturbation models involving a penalization of the first order derivatives have provided a new insight into the role played by surface energies in the study of phase transitions problems. It is known that if $W:{\mathbb R}^d \to [0,+\infty)$ grows at least linearly at infinity and it has exactly two potential wells of level zero at $a, b \in {\mathbb R}^d$, then the $\Gamma(L^1)$-limit of the family of functionals $$ {\mathcal F}_\varepsilon(u):= \begin{cases} \int_{\Omega} \left… 
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