A stochastic selection principle in case of fattening for curvature flow

Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367, Luckhaus, Stephan and Novaga, Matteo 2001. A stochastic selection principle in case of fattening for curvature flow. Calculus of Variations and Partial Differential Equations 13 (4) , pp. 405-425. 10.1007/s005260100080

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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

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer Verlag
ISSN:	0944-2669
Last Modified:	18 Oct 2022 13:13
URI:	https://orca.cardiff.ac.uk/id/eprint/13067

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