Representations of epi-Lipschitzian sets

A closed subset M of a Banach space E is epi-Lipschitzian, 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 -> R, for which Clarke's generalized gradient does not contain 0 at points in the boundary of M, i.e., such that: M = {x vertical bar f(x) <= 0}, 0 is not an element of partial derivative f (x) if x is an element of bdM. This extends the characterization previously known in finite dimension and answers to a standing question. (c) 2010 Elsevier Ltd. All rights reserved.