# 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…

## 49 Citations

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. In this paper we study the asymptotics of singularly perturbed phase-transition functionals of the form where u ∈ [0 1] is a phase-ﬁeld variable, ε k > 0 a singular-perturbation parameter ; i.e. ,…

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