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The Journal of Geometric Analysis

, Volume 16, Issue 2, pp 233–264 | Cite as

Droplet minimizers for the Cahn-Hilliard free energy functional

  • E. A. Carlen
  • M. C. Carvalho
  • R. Esposito
  • J. L. Lebowitz
  • R. Marra
Article

Abstract

We prove theorems characterizing the minimizers for the Cahn-Hilliard free energy functional, which is used to describe the liquid vapor phase transition (or the 2 state magnetization transition). In particular, we exactly determine the critical density for droplet formation, and the geometry of the droplets.

Math Subject Classifications

49S05 52A40 82B26 

Key Words and Phrases

Free energy functional critical droplet minimization problem 

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Copyright information

© Mathematica Josephina, Inc. 2006

Authors and Affiliations

  • E. A. Carlen
    • 1
    • 2
    • 3
    • 4
    • 5
  • M. C. Carvalho
    • 1
    • 2
    • 3
    • 4
    • 5
  • R. Esposito
    • 1
    • 2
    • 3
    • 4
    • 5
  • J. L. Lebowitz
    • 1
    • 2
    • 3
    • 4
    • 5
  • R. Marra
    • 1
    • 2
    • 3
    • 4
    • 5
  1. 1.School of MathematicsGeorgia TechAtlanta
  2. 2.Department of Mathematics and CMAFUniversity of LisbonLisbonPortugal
  3. 3.Dip. di MatematicaUniversità di L’AquilaCoppitoItaly
  4. 4.Departments of Mathematics and PhysicsRutgers UniversityNew Brunswick
  5. 5.Dipartimento di Fisica and Unità INFNUniversità di Roma Tor VergataRomaItaly

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