A stochastic selection principle in case of fattening for curvature flow

N Dirr, S Luckhaus, M Novaga

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20 Citations (Scopus)


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 epsilondW, in the limit epsilon --> 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.
Original languageEnglish
Pages (from-to)405-425
Number of pages21
JournalCalculus of Variations and Partial Differential Equations
Issue number4
Publication statusPublished - 2001


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