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Consistency in evolutions by crystalline curvature. (English) Zbl 0865.35146
Niezg√≥dka, Marek (ed.) et al., Free boundary problems, theory and applications. Lectures presented at the congress, Zakopane, Poland, June 11–18, 1995. Harlow: Longman. Pitman Res. Notes Math. Ser. 363, 186-202 (1996).
Summary: Motion of curves by crystalline energy is often considered for “admissible” piecewise linear curves. This is because the evolution of such curves can be described by a simple system of ordinary differential equations. Recently, a generalized notion of solutions based on comparison principle was introduced by the authors. In this note, we show that a classical admissible solution is always a generalized solution in our sense.
For the entire collection see [Zbl 0856.00025].

MSC:
35R35 Free boundary problems for PDEs
82D25 Statistical mechanical studies of crystals
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