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MiS Preprint
70/2000
A stochastic selection principle in case of fattening for curvature flow
Nicolas Dirr, Stephan Luckhaus and Matteo Novaga
Abstract
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 $\epsilon d W$, in the limit $\epsilon \to 0$ the measure selects two evolving curves, the upper and lower barrier in the sense of De Giorgi. Further we show partial results for nonzero $\epsilon$
