Regularity and convergence of crystalline motion
SIAM Journal on Mathematical Analysis
On the bolw-up rate for fast bolw-up solutions arising in an anisotropic crystalline motion
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
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Behavior of convex solution polygons to a general crystalline motion is investigated. A polygon is called admissible if the set of its normal angles equals that of the Wulff shape. We prove that if the initial polygon is not an admissible polygon, then all edges disappear simultaneously, or edge disappearing occurs at most finitely many instants and eventually a convex solution polygon becomes an admissible convex polygon. In the latter case, the normal angle of disappearing edge does not belong to the set of the normal angles of the Wulff shape. We also show five typical exmnples of this motion.