发表机构
Penn State University; Queen’s University; Politecnico di Milano（宾夕法尼亚州立大学; 女王大学; 米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有界开集的最优切片问题，证明最优切片存在且与入侵物种根除问题相关，并推导了最优性的必要条件。
AI 中文摘要
给定一个有界开集 $V\subset \mathbb{R}^2$，我们考虑用一族曲线来切片该集合的问题，使得这些曲线的平均长度尽可能小。论文的前几节证明了最优切片的存在性，并建立了与文献\cite{BMS}中考虑的从岛屿上根除入侵生物物种问题的联系。即，最优切片可以作为最小时间根除策略的极限获得。论文的第二部分推导了最优性的各种必要条件，描述了最优切片策略在 $V$ 内部和边界 $\partial V$ 附近的行为。
英文摘要
Given a bounded open set $V\subset \mathbb{R}^2$, we consider the problem of slicing this set by a family of curves, whose average length is as small as possible. The first sections of the paper prove the existence of an optimal slicing and establish a connection with the problem of eradicating an invasive biological species from an island, considered in \cite{BMS}. Namely, an optimal slicing can be obtained as a limit of minimum time eradication strategies. The second part of the paper derives various necessary conditions for optimality, describing the behavior of an optimal slicing strategy in the interior of $V$ and near the boundary $\partial V$.
Comments32 pages, 11 figures
