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A stochastic selection principle in case of fattening for curvature flow |
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| Authors: | Nicolas Dirr Stephan Luckhaus Matteo Novaga |
| Institution: | Max–Planck–Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04109 Leipzig, Germany (e-mail: ndirr@mis.mpg.de), DE Fakult?t für Mathematik und Informatik, Universit?t Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany (e-mail: stephan.luckhaus@mis.mpg.de), DE Dipartimento di Matematica, Università di Pisa, via F. Buonarotti 2, 56127 Pisa, Italy (e-mail: novaga@dm.unipi.it), IT |
| 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 . Received: 3 November 2000 / Accepted: 4 December 2000 / Published online: 23 April 2001 |
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