Generalized versions of Ilmanen lemma: Insertion of C-(1,omega) or C-loc(1,omega) functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390776" target="_blank" >RIV/00216208:11320/18:10390776 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.14712/1213-7243.2015.245" target="_blank" >https://doi.org/10.14712/1213-7243.2015.245</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2015.245" target="_blank" >10.14712/1213-7243.2015.245</a>
Alternative languages
Result language
angličtina
Original language name
Generalized versions of Ilmanen lemma: Insertion of C-(1,omega) or C-loc(1,omega) functions
Original language description
We prove that for a normed linear space X, if f(1) : X -> R is continuous and semiconvex with modulus omega, f(2) : X -> R is continuous and semiconcave with modulus omega and f(1) <= f(2), then there exists f is an element of C-(1,omega)(X) such that f(1) <= f <= f(2). Using this result we prove a generalization of Ilmanen lemma (which deals with the case omega(t) = t) to the case of an arbitrary nontrivial modulus omega. This generalization (where a C-loc(1,omega) function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Commentationes Mathematicae Universitatis Carolinae
ISSN
0010-2628
e-ISSN
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Volume of the periodical
59
Issue of the periodical within the volume
2
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
9
Pages from-to
223-231
UT code for WoS article
000446183900007
EID of the result in the Scopus database
2-s2.0-85048498004