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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10127428%21RIV13-GA0-11320___
rdf:type
skos:Concept n3:Vysledek
dcterms:description
Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$. Singular points of order $k$ of $f$ are those points at which the Clarke subdifferential of $f$ is at least $k$-dimensional. We prove that if $f$ is Clarke regu lar, then the set of all singular points of order $k$ of $f$ can be covered by countably many Lipchitz surfaces of codimension $k$. We prove also two results on arbitrary functions, which work with Hadamard directional derivatives and can be considered as generalization of the above result on Clarke regular functions. Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$. Singular points of order $k$ of $f$ are those points at which the Clarke subdifferential of $f$ is at least $k$-dimensional. We prove that if $f$ is Clarke regu lar, then the set of all singular points of order $k$ of $f$ can be covered by countably many Lipchitz surfaces of codimension $k$. We prove also two results on arbitrary functions, which work with Hadamard directional derivatives and can be considered as generalization of the above result on Clarke regular functions.
dcterms:title
Singular points of order k of Clarke regular and arbitrary functions Singular points of order k of Clarke regular and arbitrary functions
skos:prefLabel
Singular points of order k of Clarke regular and arbitrary functions Singular points of order k of Clarke regular and arbitrary functions
skos:notation
RIV/00216208:11320/12:10127428!RIV13-GA0-11320___
n3:predkladatel
n4:orjk%3A11320
n5:aktivita
n12:Z n12:P
n5:aktivity
P(GA201/09/0067), Z(MSM0021620839)
n5:cisloPeriodika
1
n5:dodaniDat
n9:2013
n5:domaciTvurceVysledku
n10:7357362
n5:druhVysledku
n16:J
n5:duvernostUdaju
n14:S
n5:entitaPredkladatele
n18:predkladatel
n5:idSjednocenehoVysledku
168147
n5:idVysledku
RIV/00216208:11320/12:10127428
n5:jazykVysledku
n7:eng
n5:klicovaSlova
Hadamard derivative; singularities; Clarke regular functions
n5:klicoveSlovo
n6:Clarke%20regular%20functions n6:singularities n6:Hadamard%20derivative
n5:kodStatuVydavatele
CZ - Česká republika
n5:kontrolniKodProRIV
[13B9CF2B1E8A]
n5:nazevZdroje
Commentationes Mathematicae Universitatis Carolinae
n5:obor
n11:BA
n5:pocetDomacichTvurcuVysledku
1
n5:pocetTvurcuVysledku
1
n5:projekt
n17:GA201%2F09%2F0067
n5:rokUplatneniVysledku
n9:2012
n5:svazekPeriodika
53
n5:tvurceVysledku
Zajíček, Luděk
n5:zamer
n19:MSM0021620839
s:issn
0010-2628
s:numberOfPages
13
n20:organizacniJednotka
11320