@inbook{689d71c1c9ee4d709bfc16be5ff71198,

title = "Singular perturbation problems involving curvature",

abstract = "Consider an anisotropic area functional, giving rise to a variational principle for the shape of crystal surfaces. Sometimes such a functional is regularised with an additional curvature term to avoid difficulties coming from a lack of convexity. We study the asymptotic behaviour of the resulting functional as the strength of the regularisation tends to 0. We consider two cases. The first corresponds to a cubic crystal structure. The expected shapes of the crystal surfaces are polyhedra with faces parallel to the coordinate planes, and for the regularised functionals, we discover a limiting energy depending on the lengths of the edges. In the second case, we have a uniaxial anisotropy. We calculate the limiting energy for surfaces of revolution and give a lower bound for topological spheres.",

author = "Roger Moser",

year = "2015",

language = "English",

isbn = "978-3-319-18572-9",

series = "Springer Proceedings in Mathematics & Statistics",

publisher = "Springer",

pages = "49--75",

editor = "Gui-Qiang Chen and Michael Grinfeld and Knops, {R. J.}",

booktitle = "Differential Geometry and Continuum Mechanics",

}