epi-Lipschitz集的表示
Representations of epi-Lipschitzian sets
摘要：
Banach空间$E$的闭子集$M$是\ep，即，可以局部表示为Lipschitz函数的上图，当且仅当它是某个局部Lipschitz函数$f: E\to \R$的水平集，其中Clarke广义梯度在$M$的边界上的点处不包含0，即，使得：M=\{x \mid f（x）\leq 0\}，0 \not \in \partial f（x）{if} x \in \bd M.这扩展了以前已知的有限维的特征，并回答了一个悬而未决的问题
英文摘要：
A closed subset $M$ of a Banach space $E$ is \ep, i.e., can be represented locally as the epigraph of a Lipschitz function, if and only if it is the level set of some locally Lipschitz function $f: E\to \R$, wich Clarke's generalized gradient does not contain 0 at points in the boundary of $M$, i.e., such that: M=\{x \mid f(x)\leq 0\}, 0\not \in \partial f(x) {if} x\in \bd M. This extends the characterization previously known in finite dimension and answers to a standing open question
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
