Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lussardi, Luca and Röger, Matthias 2016. Gamma Convergence of a Family of Surface–Director Bending Energies with Small Tilt. Archive for Rational Mechanics and Analysis, Vol. 219, Issue. 3, p. 985.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 142, Issue 4
  • August 2012, pp. 839-865

Towards a variational theory of phase transitions involving curvature

  • Roger Moser (a1)
  • DOI:
  • Published online: 10 August 2012

An anisotropic area functional is often used as a model for the free energy of a crystal surface. For models of faceting, the anisotropy is typically such that the functional becomes non-convex, and then it may be appropriate to regularize it with an additional term involving curvature. When the weight of the curvature term tends to zero, this gives rise to a singular perturbation problem.

The structure of this problem is comparable to the theory of phase transitions studied first by Modica and Mortola. Their ideas are also useful in this context, but they have to be combined with adequate geometric tools. In particular, a variant of the theory of curvature varifolds, introduced by Hutchinson, is used in this paper. This allows an analysis of the asymptotic behaviour of the energy functionals.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *