Regularity and convergence of crystalline motion

Katsuyuki Ishii, Halil Mete Soner

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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
Issue number1
StatePublished - 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


  • Crystalline motion
  • Motion by mean curvature
  • Viscosity solutions


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