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Local versus global Lipschitz geometry
Journal of the London Mathematical SocietyAbstractIn this article, we prove that for a definable set in an o‐minimal structure with connected link (at 0 or infinity), the inner distance of the link is equivalent to the inner distance of the set restricted to the link. With this result, we obtain several consequences.
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Sierpiński's hierarchy and locally Lipschitz functions
Fundamenta Mathematicae, 1995Let \(Z\) be an uncountable Polish space and let \(S_\alpha (Z)\) \((\alpha < \omega_1)\) be classes of functions \(g : Z \to R\) \((R\) -- the real line) of Sierpiński classification of Borel measurable functions. A function \(f : I \to R\) \((I\) -- an interval in \(R)\) is said to be locally Lipschitz on \(I\) if for each point \(x\) in \(I\) there ...
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Local and global Lipschitz classes
1987Let h be a modulus of continuity, i.e. u is a concave positive and increasing function. If D is a domain in \({\mathbb{R}}^ n\), then a function \(u: D\to {\mathbb{R}}\) is said to belong to the local Lipschitz class loc Lip\({}_ h(D)\) if there is \(b\in (0,1)\) and M such that \(| u(x)- u(y)| \leq M h(| x-y|)\) for all \(x\in D\) and \(y\in D\) with \
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The Lipschitz extension problem with prescribed local Lipschitz constants and eikonal mappings
Journal of Mathematical Analysis and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Backus, Aidan, Ze-An, Ng
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Hemivariational Inequalities for Locally Lipschitz Functionals
2021Z. Naniewicz, P. D. Panagiotopoulos
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