Geodesic
Motion of discrete interfaces in low-contrast random environments
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1275-1301

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We study the asymptotic behavior of a discrete-in-time minimizing movement scheme for square lattice interfaces when both the lattice spacing and the time step vanish. The motion is assumed to be driven by minimization of a weighted random perimeter functional with an additional deterministic dissipation term. We consider rectangular initial sets and lower order random perturbations of the perimeter functional. In case of stationary, α-mixing perturbations we prove a stochastic homogenization result for the interface velocity. We also provide an example which indicates that only stationary, ergodic perturbations might not yield a spatially homogenized limit velocity for this minimizing movement scheme.

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DOI : 10.1051/cocv/2017067
Classification : 53C44, 49J55, 49J45
Keywords: Minimizing movement, discrete interface motion, crystalline curvature, stochastic homogenization

Ruf, Matthias 1

1 
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     title = {Motion of discrete interfaces in low-contrast random environments},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1275--1301},
     publisher = {EDP-Sciences},
     volume = {24},
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     year = {2018},
     doi = {10.1051/cocv/2017067},
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Ruf, Matthias. Motion of discrete interfaces in low-contrast random environments. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1275-1301. doi: 10.1051/cocv/2017067

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