Examples and counterexamples in Lipschitz analysis

In the analysis of functions and multi-valued map­ pings of Lipschitzian type, there are many different notions of Lip­ schitz behav ior , regularity and generali zed derivatives. We collect relevant examples illu strating the interrelations between various con­ cepts, the differences with the smooth case, a nd the importance of certain assumptions a nd special classes of Lipschitz mappings in ap­ pl ications. K eywords: Lipschitz ( rnul t i- )functions, regularity co ucepts, generalized deriva tiv es , application to stationa ry points, pathologi­ cal Lipschitz functions .

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