Examples and counterexamples in Lipschitz analysis

Abstract: In the analysis of functions and multi-valued map-pings of Lipschitzian type, there are many different notions of Lip-schitz behavior, regularity and generalized derivatives. We collect relevant examples illustrating the interrelations between various con-cepts, the differences with the smooth case, and the importance of certain assumptions and special classes of Lipschitz mappings in ap-plications. K eywords: Lipschitz ( rnul t i-)functions, regularity coucepts, generalized derivatives, application to sta tionary points, pathologi-cal Lipschitz functions. 1.