Clarke critical values of subanalytic Lipschitz continuous functions
Volume 87 / 2005
Annales Polonici Mathematici 87 (2005), 13-25
MSC: Primary 35B38; Secondary 49J52, 32B30.
DOI: 10.4064/ap87-0-2
Abstract
The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawłucki's extension of the Puiseux lemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of “broadly critical” points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.
