2 00 9 Invariance of Regularity Conditions under Definable , Locally Lipschitz , Weakly Bi - Lipschitz Mappings

Bi-Lipschitz Mappings and Quasinearly Subharmonic Functions

After considering a variant of the generalized mean value inequality of quasinearly subharmonic functions, we consider certain invariance properties of quasinearly subharmonic functions. Kojić has shown that in the plane case both the class of quasinearly subharmonic functions and the class of regularly oscillating functions are invariant under conformal mappings. We give partial generalization...

On Inverses of -convex Mappings

In the first part of this paper, we prove that in a sense the class of bi-Lipschitz δ-convex mappings, whose inverses are locally δ-convex, is stable under finite-dimensional δ-convex perturbations. In the second part, we construct two δ-convex mappings from l1 onto l1, which are both bi-Lipschitz and their inverses are nowhere locally δ-convex. The second mapping, whose construction is more co...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Nonsmooth Equations in Optimization Nonconvex Optimization and Its Applications

The titles published in this series are listed at the end of this volume. 1 1 2 4 4 4 5 5 6 6 7 9 Multifunctions and Derivatives Particular Locally Lipschitz Functions and Related Definitions Generalized Jacobians of Locally Lipschitz Functions Pseudo-Smoothness and D°f Piecewise Functions NCP Functions 1.4 Definitions of Regularity Definitions of Lipschitz Properties Regularity Definitions Fun...

A Schoenflies Extension Theorem for a Class of Locally Bi-lipschitz Homeomorphisms

In this paper we prove a new version of the Schoenflies extension theorem for collared domains Ω and Ω in Rn: for p ∈ [1, n), locally bi-Lipschitz homeomorphisms from Ω to Ω with locally p-integrable, second-order weak derivatives admit homeomorphic extensions of the same regularity. Moreover, the theorem is essentially sharp. The existence of exotic 7-spheres shows that such extension theorems...