Asymptotics for optimal controls for horizontal mean curvature flow
Analysis of PDEs
2020-05-22 v1 Optimization and Control
Abstract
The solutions to surface evolution problems like mean curvature flow can be expressed as value functions of suitable stochastic control problems, obtained as limit of a family of regularised control problems. The control-theoretical approach is particularly suited for such problems for degenerate geometries like the Heisenberg group. In this situation a new type of singularities absent for the Euclidean mean curvature flow occurs, the so-called characteristic points. This paper investigates the asymptotic behaviour of the regularised optimal controls in the vicinity of such characteristic points.
Cite
@article{arxiv.2005.10599,
title = {Asymptotics for optimal controls for horizontal mean curvature flow},
author = {Nicolas Dirr and Federica Dragoni and Raffaele Grande},
journal= {arXiv preprint arXiv:2005.10599},
year = {2020}
}