A remark on the compactness for the Cahn–Hilliard functional

Giovanni Leoni

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 2, page 517-523
  • ISSN: 1292-8119

Abstract

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

How to cite

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Leoni, Giovanni. "A remark on the compactness for the Cahn–Hilliard functional." ESAIM: Control, Optimisation and Calculus of Variations 20.2 (2014): 517-523. <http://eudml.org/doc/272825>.

@article{Leoni2014,
abstract = {In this note we prove compactness for the Cahn–Hilliard functional without assuming coercivity of the multi-well potential.},
author = {Leoni, Giovanni},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {singular perturbations; gamma-convergence; compactness; Cahn-Hilliard functional},
language = {eng},
number = {2},
pages = {517-523},
publisher = {EDP-Sciences},
title = {A remark on the compactness for the Cahn–Hilliard functional},
url = {http://eudml.org/doc/272825},
volume = {20},
year = {2014},
}

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
PB - EDP-Sciences
VL - 20
IS - 2
SP - 517
EP - 523
AB - In this note we prove compactness for the Cahn–Hilliard functional without assuming coercivity of the multi-well potential.
LA - eng
KW - singular perturbations; gamma-convergence; compactness; Cahn-Hilliard functional
UR - http://eudml.org/doc/272825
ER -

References

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  1. [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. Zbl0779.35011MR1152723
  2. [2] S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn–Hilliard fluids. Ann. Inst. Henri Poincaré Anal. Non Linéaire7 (1990) 67–90. Zbl0702.49009MR1051228
  3. [3] A. Braides, Gamma-convergence for beginners, vol. 22 of Oxford Lect. Ser. Math. Appl. Oxford University Press, New York (2002). Zbl1198.49001MR1968440
  4. [4] I. Fonseca and L. Tartar, The gradient theory of phase transitions for systems with two potential wells. Proc. Roy. Soc. Edinburgh Sect. A111 (1989) 89–102. Zbl0676.49005MR985992
  5. [5] M.E. Gurtin, Some results and conjectures in the gradient theory of phase transitions. IMA, preprint 156 (1985). Zbl0634.49019MR870014
  6. [6] G. Leoni, A first course in Sobolev spaces, vol. 105 of Graduate Stud. Math. American Mathematical Society (AMS), Providence, RI (2009). Zbl1180.46001MR2527916
  7. [7] L. Modica and S. Mortola, Un esempio di Γ-convergenza. (Italian). Boll. Un. Mat. Ital. B 14 (1977) 285–299. Zbl0356.49008MR445362
  8. [8] L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal.98 (1987) 123–142. Zbl0616.76004MR866718
  9. [9] P. Sternberg, The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal.101 (1988) 209–260. Zbl0647.49021MR930124

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