On almost everywhere differentiability of the metric projection on closed sets in lp (Rn), 2 < p< ∞

Autor:	Sjödin, Tord
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles normed space uniform convexity closed set metric projection lp-space Fréchet differential Lipschitz condition
Druh dokumentu:	Non-fiction
ISSN:	0011-4642
Abstrakt:	Abstract: Let F be a closed subset of R n and let P(x) denote the metric projection (closest point mapping) of x E R n onto F in l p -norm. A classical result of Asplund states that P is (Fréchet) differentiable almost everywhere (a.e.) in R n in the Euclidean case p = 2. We consider the case 2 < p < ∞ and prove that the ith component Pi(x) of P(x) is differentiable a.e. if Pi(x) 6= xi and satisfies Hölder condition of order 1/(p−1) if Pi(x) = xi .
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Full text from SpringerLink