Calculus of Variations and Geometric Measure Theory

N. Dirr - S. Luckhaus - M. Novaga

A stochastic selection principle in case of fattening for curvature flow

created on 14 Dec 2002
modified by novaga on 10 Nov 2018


Published Paper

Inserted: 14 dec 2002
Last Updated: 10 nov 2018

Journal: Calc. Var. and Partial Differential Eqs.
Volume: 13
Number: 4
Pages: 405-425
Year: 2001


Consider two disjoint circles moving by mean curvature plus a forcing term which makes them touch with zero velocity. It is known that the generalized solution in the viscosity sense ceases to be a curve after the touching (the so-called fattening phenomenon). We show that after adding a small stochastic forcing $\eps \d W$, in the limit $\eps\to 0$ the measure selects two evolving curves, the upper and lower barrier in the sense of De Giorgi. Further we show partial results for nonzero $\eps.$