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PreprintCC BY-NC-ND 4.0arXiv

On the Value Function for a Class of Set Motion Problems

  • Alberto Bressan
  • Maria Teresa Chiri
  • Elsa M. Marchini
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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.

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Cite

BibTeXRIS
BibTeX
@misc{bressan2026value,
  title = {{On the Value Function for a Class of Set Motion Problems}},
  author = {Alberto Bressan and Maria Teresa Chiri and Elsa M. Marchini},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36133},
  eprint = {2609.36133},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36133},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the Value Function for a Class of Set Motion Problems
AU  - Alberto Bressan
AU  - Maria Teresa Chiri
AU  - Elsa M. Marchini
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.36133
UR  - https://arxiv.org/abs/2609.36133
AB  - 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.
ER  -