We describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.
Cite this article
Andrea Braides, Andrea Malchiodi, Curvature theory of boundary phases: the two-dimensional case. Interfaces Free Bound. 4 (2002), no. 4, pp. 345–370DOI 10.4171/IFB/65