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Towards a variational theory of phase transitions involving curvature


Reference:

Moser, R., 2012. Towards a variational theory of phase transitions involving curvature. Proceedings of the Royal Society of Edinburgh Section A - Mathematics, 142 (4), pp. 839-865.

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    Official URL:

    http://dx.doi.org/10.1017/S0308210510000995

    Abstract

    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 nonconvex, and then it may be appropriate to regularize it with an additional term involving curvature. When the weight of the curvature term tends to 0, 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 use- ful in this context, but they have to be combined with adequate geometric tools. In particular, a variant of the theory of curvature varifolds, intro- duced by Hutchinson, is used in this paper. This allows an analysis of the asymptotic behaviour of the energy functionals.

    Details

    Item Type Articles
    CreatorsMoser, R.
    DOI10.1017/S0308210510000995
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementMoser_PRSEA_2011.pdf: Copyright (2011) Royal Society of Edinburgh. This paper has been accepted for publication and will appear in a revised form, subsequent to editorial input by Cambridge University Press, in 'Proceedings of the Royal Society of Edinburgh, Section: A Mathematics' published by Cambridge University Press.
    RefereedYes
    StatusPublished
    ID Code23333

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