Asymptotics for optimal controls for horizontal mean curvature flow

Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367, Dragoni, Federica ORCID: https://orcid.org/0000-0001-6076-9725 and Grande, Raffaele 2021. Asymptotics for optimal controls for horizontal mean curvature flow. Nonlinear Analysis 202 , 112076. 10.1016/j.na.2020.112076

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Elsevier
ISSN:	0362-546X
Date of First Compliant Deposit:	19 December 2024
Date of Acceptance:	23 July 2020
Last Modified:	16 Jan 2025 15:45
URI:	https://orca.cardiff.ac.uk/id/eprint/174866

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