TY  - JOUR
AB  - We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. For the first time, we are able to construct martingale solutions which satisfy the equation pointwise and not only in a generalized (distributional or viscosity) sense. Moreover, we study their large-time behavior. Our analysis is based on a viscous approximation and new global bounds, namely, an L-w,x,t(infinity) estimate for the gradient and an L-w, x,t(2) bound for the Hessian. The proof makes essential use of the delicate interplay between the deterministic mean curvature part and the stochastic perturbation, which permits to show that certain gradient-dependent energies are supermartingales. Our energy bounds in particular imply that solutions become asymptotically spatially homogeneous and approach a Brownian motion perturbed by a random constant.
DA  - 2021
DO  - 10.1007/s00440-020-01012-6
LA  - eng
M2  - 407
PY  - 2021
SP  - 407-449
T2  - Probability Theory and Related Fields
TI  - Existence of martingale solutions and large-time behavior for a stochastic mean curvature flow of graphs
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29374714
Y2  - 2024-11-22T08:08:22
ER  -