Singular points of order k of Clarke regular and arbitrary functions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10127428" target="_blank" >RIV/00216208:11320/12:10127428 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Singular points of order k of Clarke regular and arbitrary functions

Original language 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F09%2F0067" target="_blank" >GA201/09/0067: Theory of real functions and descriptive set theory II</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Commentationes Mathematicae Universitatis Carolinae

ISSN

0010-2628

e-ISSN

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Volume of the periodical

53

Issue of the periodical within the volume

1

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

13

Pages from-to

51-63

UT code for WoS article

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EID of the result in the Scopus database

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