In this note we prove compactness for the Cahn-Hilliard functional without assuming coercivity of the multi-well potential.
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] An extension theorem from connected sets, and homogenization in general periodic domains. Nonlinear Anal. 18 (1992) 481-496. | MR | Zbl
, , and ,[2] 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] Gamma-convergence for beginners, vol. 22 of Oxford Lect. Ser. Math. Appl. Oxford University Press, New York (2002). | MR | Zbl
,[4] The gradient theory of phase transitions for systems with two potential wells. Proc. Roy. Soc. Edinburgh Sect. A 111 (1989) 89-102. | MR | Zbl
and ,[5] Some results and conjectures in the gradient theory of phase transitions. IMA, preprint 156 (1985). | MR | Zbl
,[6] A first course in Sobolev spaces, vol. 105 of Graduate Stud. Math. American Mathematical Society (AMS), Providence, RI (2009). | MR | Zbl
,[7] Un esempio di Γ-convergenza. (Italian). Boll. Un. Mat. Ital. B 14 (1977) 285-299. | MR | Zbl
and ,[8] The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987) 123-142. | MR | Zbl
,[9] The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal. 101 (1988) 209-260. | MR | Zbl
,Cité par Sources :