Calculus of Variations and Geometric Measure Theory

F. Boarotto - L. Caravenna - F. Rossi - D. Vittone

On the Lebesgue measure of the boundary of the evoluted set

created by vittone on 15 Jul 2021
modified on 24 Mar 2022


Published Paper

Inserted: 15 jul 2021
Last Updated: 24 mar 2022

Journal: Systems Control Lett.
Volume: 158
Number: Paper No. 105078
Pages: 5
Year: 2021

ArXiv: 2107.06739 PDF


The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the evoluted set has negligible boundary (i.e. its Lebesgue measure is zero). We also provide several counterexample showing that the hypotheses of our theorem are close to sharp.