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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 -&gt; R is continuous and semiconvex with modulus omega, f(2) : X -&gt; R is continuous and semiconcave with modulus omega and f(1) &lt;= f(2), then there exists f is an element of C-(1,omega)(X) such that f(1) &lt;= f &lt;= 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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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