Regularity and convergence of crystalline motion

Katsuyuki Ishii, Halil Mete Soner

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)19-37
Number of pages19
JournalSIAM Journal on Mathematical Analysis
Volume30
Issue number1
DOIs
StatePublished - Jan 1 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Crystalline motion
  • Motion by mean curvature
  • Viscosity solutions

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