On the dynamics of crystalline motion

Abstract: "Solids can exist in polygonal shapes with boundaries unions of flat pieces called facets. Analyzing the growth of such crystalline shapes is an important problem in materials science. In this paper we derive equations that govern the evolution of such shapes; we formulate the corresponding initial-value problem variationally; and we use this formulation to establish a comparison principle for crystalline evolutions. This principle asserts that two evolving crystals one initially inside the other will remain in that configuration for all time.