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 that is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive a uniform bound for the diffuse surface area, prove the tightness of solutions in the sharp interface limit, and show the convergence to phase-indicator functions.
Original languageEnglish
Pages (from-to)175-203
JournalStochastic Partial Differential Equations: Analysis and Computations
Volume1
Issue number1
DOIs
Publication statusPublished - 1 Mar 2013

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