Regularity and Convergence of Crystalline Motion

Regularity and Convergence of Crystalline Motion

We consider the motion of polygons by crystalline curvature. We show that "smooth" polygon evolves by crystalline curvature "smoothly" and that it shrinks to a point in finite time. We also establish the convergence of crystalline motion to the motion by mean curvature.

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Veröffentlicht in:SIAM journal on mathematical analysis 1998, Vol.30 (1), p.19-37
Hauptverfasser: Ishii, Katsuyuki, Soner, Halil Mete
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Energy
Phase transitions
Polygons
Viscosity
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Zusammenfassung:We consider the motion of polygons by crystalline curvature. We show that "smooth" polygon evolves by crystalline curvature "smoothly" and that it shrinks to a point in finite time. We also establish the convergence of crystalline motion to the motion by mean curvature.
ISSN:0036-1410
1095-7154
DOI:10.1137/S0036141097317347