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A remark on the compactness for the Cahn–Hilliard functional

  • Giovanni Leoni (a1)

Abstract

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

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[1] Acerbi, E., Chiadò Piat, V., Dal Maso, G. and Percivale, D., An extension theorem from connected sets, and homogenization in general periodic domains. Nonlinear Anal. 18 (1992) 481496.
[2] Baldo, S., Minimal interface criterion for phase transitions in mixtures of Cahn–Hilliard fluids. Ann. Inst. Henri Poincaré Anal. Non Linéaire 7 (1990) 6790.
[3] A. Braides, Gamma-convergence for beginners, vol. 22 of Oxford Lect. Ser. Math. Appl. Oxford University Press, New York (2002).
[4] Fonseca, I. and Tartar, L., The gradient theory of phase transitions for systems with two potential wells. Proc. Roy. Soc. Edinburgh Sect. A 111 (1989) 89102.
[5] Gurtin, M.E., Some results and conjectures in the gradient theory of phase transitions. IMA, preprint 156 (1985).
[6] G. Leoni, A first course in Sobolev spaces, vol. 105 of Graduate Stud. Math. American Mathematical Society (AMS), Providence, RI (2009).
[7] Modica, L. and Mortola, S., Un esempio di Γ-convergenza. (Italian). Boll. Un. Mat. Ital. B 14 (1977) 285299.
[8] Modica, L., The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987) 123142.
[9] Sternberg, P., The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal. 101 (1988) 209260.

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A remark on the compactness for the Cahn–Hilliard functional

  • Giovanni Leoni (a1)

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