Corners in phase-field theory

Phase-field models for strongly anisotropic surface energy need to be regularized remove the ill posedness of dynamic equations. Regularization introduces a new length scale, corner size, also called bending length. For large with respect interface thickness, phase-field method is known converge asymptotically toward sharp-interface theory when appropriate approximation Willmore used. In this work we study opposite limit, i.e., size smaller than width, and show that shape corners, at equilibrium, differs from picture. However, find phase transition preserved presents same properties as classical problem.