ESSENTIALLY SMOOTH LIPSCHITZ FUNCTIONS

In this paper we address some of the most fundamental questions regard ing the differentiability structure of locally Lipschitz functions def ined on separable Banach spaces. For example, we examine the relations hip between integrability, D-representability, and strict differentiab ility. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipschitz functions that are integrable, D-representable and possess desirable differentiability p roperties. We also present some striking applications of our results t o distance functions. (C) 1997 Academic Press.