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Convex Extension Preserving Lipschitz Constant

✍ Scribed by Witold Rzymowski

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 169 KB
Volume: 212
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5093

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✦ Synopsis

Let ⍀ ; ‫ޒ‬ n be a non-empty bounded open and convex set and let f be a real function defined on the boundary of the set ⍀. A necessary and sufficient condition is given for f to be extendable to a convex and lipschitzian function defined on the whole space ‫ޒ‬ n . The solution u to the degenerate case of the w 2 x Monge᎐Ampere equation det Ѩ urѨ x Ѩ x s 0, u s f on the boundary of ⍀, is ´i j lipschitzian if and only if f satisfies this condition.

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