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.

Accepted:

DOI: 10.1051/cocv/2017067

Keywords: Minimizing movement, discrete interface motion, crystalline curvature, stochastic homogenization

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@article{COCV_2018__24_3_1275_0, author = {Ruf, Matthias}, 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}, number = {3}, year = {2018}, doi = {10.1051/cocv/2017067}, zbl = {1450.49008}, mrnumber = {3877202}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017067/} }

TY - JOUR AU - Ruf, Matthias TI - Motion of discrete interfaces in low-contrast random environments JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1275 EP - 1301 VL - 24 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017067/ DO - 10.1051/cocv/2017067 LA - en ID - COCV_2018__24_3_1275_0 ER -

%0 Journal Article %A Ruf, Matthias %T Motion of discrete interfaces in low-contrast random environments %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1275-1301 %V 24 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017067/ %R 10.1051/cocv/2017067 %G en %F COCV_2018__24_3_1275_0

Ruf, Matthias. Motion of discrete interfaces in low-contrast random environments. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 3, pp. 1275-1301. doi : 10.1051/cocv/2017067. http://archive.numdam.org/articles/10.1051/cocv/2017067/

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