Work

On the Value Function for a Class of Set Motion Problems

Year: 2026

Type: preprint

Abstract: The paper considers a class of optimal set motion problems, where the control determines the velocity of boundary points in the normal direction. Results and counterexamples are given, on the continuous dependence of the minimum cost from the initial configuration. The last sections of the paper study the slicing cost of bounded open sets. For strongly Lipschitz domains, it is proved that the slicing cost varies continuously w.r.t. the Hausdorff distance of the boundaries. We conjecture that the slicing cost for a disc is maximal among all sets with the same area.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.36133

Authors: Bressan, Alberto, Chiri, Maria Teresa, Marchini, Elsa M.

Institutions: Pennsylvania State University, Queen's University, Politecnico di Milano

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214961597

Cites: 1

Cited by:

Related to: 10