A stochastic selection principle in case of fattening for curvature flow

Nicolas Dirr, Stephan Luckhaus, and Matteo Novaga

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Submission date: 06. Nov. 2000
Pages: 21
published in: Calculus of variations and partial differential equations, 13 (2001) 4, p. 405-425 
DOI number (of the published article): 10.1007/s005260100080
Bibtex
Keywords and phrases: stochastic mean curvature flow, fattening
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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 , in the limit the measure selects two evolving curves, the upper and lower barrier in the sense of De Giorgi. Further we show partial results for nonzero