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 \(\epsilon {\rm d} W\), 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 \(\epsilon\).
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Received: 3 November 2000 / Accepted: 4 December 2000 / Published online: 23 April 2001
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Dirr, N., Luckhaus, S. & Novaga, M. A stochastic selection principle in case of fattening for curvature flow. Calc Var 13, 405–425 (2001). https://doi.org/10.1007/s005260100080
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DOI: https://doi.org/10.1007/s005260100080