Displaying similar documents to “Nonconvex sweeping process.”

Lipschitz sums of convex functions

Marianna Csörnyei, Assaf Naor (2003)

Studia Mathematica

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We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.

Spectral gap and convex concentration inequalities for birth–death processes

Wei Liu, Yutao Ma (2009)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we consider a birth–death process with generator ℒ and reversible invariant probability. Given an increasing function and the associated Lipschitz norm ‖⋅‖, we find an explicit formula for ∥ ( - ℒ ) - 1 ∥ Lip ( ρ ) . As a typical application, with spectral theory, we revisit one variational formula of M. F. Chen for the spectral gap of ℒ in (). Moreover, by Lyons–Zheng’s forward-backward martingale decomposition theorem, we get convex concentration inequalities for additive functionals...

Lower semicontinuous differential inclusions

Tzanko Donchev (1998)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In the paper we consider lower semicontinuous differential inclusions with one sided Lipschitz and compact valued right hand side in a Banach space with uniformly convex dual. We examine the nonemptiness and some qualitative properties of the solution set.