Towards a variational theory of phase transitions involving curvature

Roger Moser
2012 Proceedings of the Royal Society of Edinburgh. Section A Mathematics  
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
more » ... ortola. 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.
doi:10.1017/s0308210510000995 fatcat:srmoivmhmjhibhss6lhsw6bciu