标题： 关于最优动态阻塞策略的正则性 显示英文标题

标题： On the Regularity of Optimal Dynamic Blocking Strategies

摘要： 本文研究了一个动态阻塞问题，该问题受到最优防火隔离模型的启发。 虽然火势可以在所有方向以单位速度扩展，但屏障是在实时构建的。 寻求一种最优策略，以最小化燃烧区域的总价值加上建设成本。 众所周知，存在最优屏障。 一般来说，它们是可数个紧致、连通、可求长集合的并集。 本文的主要结果表明，最优屏障在任何地方都是稀疏的。 证明依赖于对可达集和火势最优轨迹的新估计，解决了在障碍物存在情况下的最短时间问题。 显示英文摘要

摘要： 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.