### Abstract

Original language | English |
---|---|

Pages (from-to) | 405-425 |

Number of pages | 21 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 13 |

Issue number | 4 |

Publication status | Published - 2001 |

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### Cite this

*Calculus of Variations and Partial Differential Equations*,

*13*(4), 405-425.

**A stochastic selection principle in case of fattening for curvature flow.** / Dirr, N; Luckhaus, S; Novaga, M.

Research output: Contribution to journal › Article

*Calculus of Variations and Partial Differential Equations*, vol. 13, no. 4, pp. 405-425.

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TY - JOUR

T1 - A stochastic selection principle in case of fattening for curvature flow

AU - Dirr, N

AU - Luckhaus, S

AU - Novaga, M

N1 - ID number: ISI:000173196000001

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

M3 - Article

VL - 13

SP - 405

EP - 425

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 4

ER -