A remark on the compactness for the Cahn-Hilliard functional
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 517-523.

In this note we prove compactness for the Cahn-Hilliard functional without assuming coercivity of the multi-well potential.

DOI : 10.1051/cocv/2013073
Classification : 49J45, 26B30
Mots-clés : singular perturbations, gamma-convergence, compactness
@article{COCV_2014__20_2_517_0,
     author = {Leoni, Giovanni},
     title = {A remark on the compactness for the {Cahn-Hilliard} functional},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {517--523},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {2},
     year = {2014},
     doi = {10.1051/cocv/2013073},
     mrnumber = {3264214},
     zbl = {1286.49014},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2013073/}
}
TY  - JOUR
AU  - Leoni, Giovanni
TI  - A remark on the compactness for the Cahn-Hilliard functional
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2014
SP  - 517
EP  - 523
VL  - 20
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv/2013073/
DO  - 10.1051/cocv/2013073
LA  - en
ID  - COCV_2014__20_2_517_0
ER  - 
%0 Journal Article
%A Leoni, Giovanni
%T A remark on the compactness for the Cahn-Hilliard functional
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2014
%P 517-523
%V 20
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv/2013073/
%R 10.1051/cocv/2013073
%G en
%F COCV_2014__20_2_517_0
Leoni, Giovanni. A remark on the compactness for the Cahn-Hilliard functional. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 517-523. doi : 10.1051/cocv/2013073. http://www.numdam.org/articles/10.1051/cocv/2013073/

[1] E. Acerbi, V. Chiadò Piat, G. Dal Maso and D. Percivale, An extension theorem from connected sets, and homogenization in general periodic domains. Nonlinear Anal. 18 (1992) 481-496. | MR | Zbl

[2] S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids. Ann. Inst. Henri Poincaré Anal. Non Linéaire 7 (1990) 67-90. | Numdam | MR | Zbl

[3] A. Braides, Gamma-convergence for beginners, vol. 22 of Oxford Lect. Ser. Math. Appl. Oxford University Press, New York (2002). | MR | Zbl

[4] I. Fonseca and L. Tartar, The gradient theory of phase transitions for systems with two potential wells. Proc. Roy. Soc. Edinburgh Sect. A 111 (1989) 89-102. | MR | Zbl

[5] M.E. Gurtin, Some results and conjectures in the gradient theory of phase transitions. IMA, preprint 156 (1985). | MR | Zbl

[6] G. Leoni, A first course in Sobolev spaces, vol. 105 of Graduate Stud. Math. American Mathematical Society (AMS), Providence, RI (2009). | MR | Zbl

[7] L. Modica and S. Mortola, Un esempio di Γ-convergenza. (Italian). Boll. Un. Mat. Ital. B 14 (1977) 285-299. | MR | Zbl

[8] L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987) 123-142. | MR | Zbl

[9] P. Sternberg, The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal. 101 (1988) 209-260. | MR | Zbl

Cité par Sources :