On the singular limit in a phase field model of phase transitions
Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 2, pp. 141-178. 
@article{AIHPC_1988__5_2_141_0,
     author = {Alikakos, Nicholas D. and Bates, Peter W.},
     title = {On the singular limit in a phase field model of phase transitions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {141--178},
     publisher = {Gauthier-Villars},
     volume = {5},
     number = {2},
     year = {1988},
     mrnumber = {954469},
     zbl = {0696.35060},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1988__5_2_141_0/}
}
TY  - JOUR
AU  - Alikakos, Nicholas D.
AU  - Bates, Peter W.
TI  - On the singular limit in a phase field model of phase transitions
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1988
SP  - 141
EP  - 178
VL  - 5
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1988__5_2_141_0/
LA  - en
ID  - AIHPC_1988__5_2_141_0
ER  - 
%0 Journal Article
%A Alikakos, Nicholas D.
%A Bates, Peter W.
%T On the singular limit in a phase field model of phase transitions
%J Annales de l'I.H.P. Analyse non linéaire
%D 1988
%P 141-178
%V 5
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1988__5_2_141_0/
%G en
%F AIHPC_1988__5_2_141_0
Alikakos, Nicholas D.; Bates, Peter W. On the singular limit in a phase field model of phase transitions. Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 2, pp. 141-178. http://www.numdam.org/item/AIHPC_1988__5_2_141_0/

[Am] H. Amann, Dual Semigroups and Second Order Linear Elliptic Boundary Value Problems, Israel J. Math., Vol. 45, 1983, pp. 225-254. | MR | Zbl

[AS] N.D. Alikakos and K.C. Shaing, On the Singular Limit for a Class of Problems Modelling Phase Transitions, S.I.A.M. J. Math. Analysis, Vol. 18, No 5, Sept. 1987, pp. 1453-1462. | MR | Zbl

[ASi] N.D. Alikakos and H. Simpson, A Variational Approach for a Class of Singular Perturbation Problems and Applications, Proc. Royal Soc. Edinburgh, 107 A, 1987, pp. 27-42. | MR | Zbl

[C] G. Caginalp, An Analysis of a Phase Field Model of a Free Boundary, Archive for Rational Mechanics and Analysis, Arch. Rat. Mech. Anal., 92, 1986, pp. 205-245. | MR | Zbl

[CF] G. Caginalp and P. Fife, Elliptic Problems Involving Phase Boundaries Satisfying a Curvature Condition, preprint. | MR | Zbl

[CM] G. Caginalp and J.B. Mcleod, The Interior Transition Layer for an Ordinary Differential Equation Arising from Solidification Theory, Quarterly of Applied Math (to appear). | MR | Zbl

[FH] G. Fusco and J. Hale, Stable Equilibria in a Scalar Parabolic Equation with Variable Diffusion, S.I.A.M. J. Math. Anal., Vol. 16, 1985, pp. 1152-1164. | MR | Zbl

[MN] J.J. Mahony and J. Norbury, Asymptotic Location of Nodal lines Using Geodesic Theory, J. Australian Math. Soc., Vol. A, January 1986. | MR | Zbl

[M1] L., Modica, Gradient Theory of Phase Transitions and Minimal Interface Criterion, Arch. Rat. Mech. Anal., 98, 1987, pp. 123-142. | MR | Zbl

[M2] L. Modica, Gradient Theory of Phase Transitions with Boundary Contact Energy (to appear). | Numdam | Zbl

[MM] L. Modica and S. Mortola, The Γ-Convergence of Some Functionals, Istituto Matematico "Leonida Tonelli", Univ. Pisa Preprint 77-7, 1977. | MR

[N] I.P. Natanson, Theory of Functions of a Real Vairable, F. Ungar Publishing Co., New York, 1955. | MR | Zbl

[S] P. Sternberg, The Effect of a Singular Perturbation on Nonconvex Variational Problems, Ph. D. dissertation, N.Y.U., June 1986.