Calculus of Variations and Geometric Measure Theory
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A. Bressan - M. T. Chiri

On the Regularity of Optimal Dynamic Blocking Strategies

created by chiri on 25 Nov 2020
modified on 23 Nov 2021


Accepted Paper

Inserted: 25 nov 2020
Last Updated: 23 nov 2021

Journal: Calc. Var. Partial Diff. Equations
Year: 2021


The paper studies a dynamic blocking problem, motivated by a model of optimal fire confinement. While the fire can expand with unit speed in all directions, barriers are constructed in real time. An optimal strategy is sought, minimizing the total value of the burned region, plus a construction cost. It is well known that optimal barriers exists. In general, they are a countable union of compact, connected, rectifiable sets. The main result of the present paper shows that optimal barriers are nowhere dense. The proof relies on new estimates on the reachable sets and on optimal trajectories for the fire, solving a minimum time problem in the presence of obstacles.


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