English

Tightness for a stochastic Allen--Cahn equation

Analysis of PDEs 2016-06-02 v4 Probability

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.

Keywords

Cite

@article{arxiv.0911.5706,
  title  = {Tightness for a stochastic Allen--Cahn equation},
  author = {Matthias Röger and Hendrik Weber},
  journal= {arXiv preprint arXiv:0911.5706},
  year   = {2016}
}

Comments

27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.6

R2 v1 2026-06-21T14:17:50.416Z