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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