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arXiv · 0911.5706

Tightness for a stochastic Allen--Cahn equation

Matthias Röger·Hendrik Weber
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Abstract

We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds and prove tightness of of solutions in the sharp interface limit, and show convergence to phase-indicator functions.

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Matthias Röger, Hendrik Weber. 2012-12-17. Tightness for a stochastic Allen--Cahn equation. https://doi.org/10.1007/s40072-013-0004-4

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