A stochastic selection principle in case of fattening for curvature flow

Reference:

Dirr, N., Luckhaus, S. and Novaga, M., 2001. A stochastic selection principle in case of fattening for curvature flow. Calculus of Variations and Partial Differential Equations, 13 (4), pp. 405-425.

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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 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.

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