Representations of epi-Lipschitzian sets
Abstract
A closed subset M of a Banach space E is , 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 , wich Clarke's generalized gradient does not contain 0 at points in the boundary of M, i.e., such that: M=\x f(x)≤ 0\, 0 ∈ ∂ f(x) if x∈ M. This extends the characterization previously known in finite dimension and answers to a standing open question
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