Wednesday, June 5, 2019 - 14:00 in V3-201
Stochastic Mean Curvature Flow of Graphs
A talk in the Bielefeld Stochastic Afternoon series by
Nils Dabrock from Dortmund
| Abstract: |
In this talk we consider a stochastic mean curvature flow of graphs over a periodic domain. Our main result is a maximum principle for the gradient and an $L^2_{\omega, x, t}$ bound for the Hessian of solutions. Furthermore, we show that variational theory can be used to treat a viscous approximation of the equation.
We use these bounds and the interpretation as a variational SPDE to extend an existence proof for two dimensions to arbitrary dimensions and obtain strong martingale solutions for this problem. In addition, we describe the large-time behavior of solutions.
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