A stochastic selection principle in case of fattening for curvature flow

N Dirr, S Luckhaus, M Novaga

Research output: Contribution to journalArticle

19 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)405-425
Number of pages21
JournalCalculus of Variations and Partial Differential Equations
Volume13
Issue number4
Publication statusPublished - 2001

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Curvature Flow
Selection Principles
Viscosity
Curve
Forcing Term
Generalized Solution
Mean Curvature
Forcing
Disjoint
Circle
Partial
Zero

Cite this

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

In: Calculus of Variations and Partial Differential Equations, Vol. 13, No. 4, 2001, p. 405-425.

Research output: Contribution to journalArticle

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