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Continuous Interpolation of Solutions of Lipschitz Inclusions

โœ Scribed by Mireille Broucke; Ari Arapostathis

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
85 KB
Volume
258
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

We show that given any finite set of trajectories of a Lipschitz differential inclusion there exists a continuous selection from the set of its solutions that interpolates the given trajectories. In addition, we present a result on lipschitzian selections.

๐Ÿ“œ SIMILAR VOLUMES

Automatic Continuity of Lipschitz Algebr
Automatic Continuity of Lipschitz Algebras
โœ B. Pavlovic ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 980 KB

For a compact metric space \((K, d), \alpha \in(0,1]\) and \(f \in C(K)\), let \(p_{x}(f)=\) \(\sup \left\{|f(t)-f(s)| d(t, s)^{x}: t, s \in K\right\}\). The set \(\operatorname{Lip}_{x}(K, d)=\left\{f \in C(K): p_{x}(f)<\infty\right\}\) with the norm \(\|f\|_{x}=|f|_{\kappa}+p_{x}(f)\) is a Banach