Curvature theory of boundary phases: the two-dimensional case
Andrea Braides, Andrea Malchiodi · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2002
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.