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Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F05%3A00001490" target="_blank" >RIV/00216208:11320/05:00001490 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$

  • Original language description

    For continuous functions $g:[0,1]timesertoer$ we prove that the functional $Phi(u)=int_0^1 gbigl(x,u(x)bigr) d x$ is weakly continuous on $W^{1,p}_0(0,1)$, $1leq p lt infty$, if and only if $g$ is linear in the second variable.

  • Czech name

    Integrální funkcionály, které jsou spojité vyhledem ke slabé topologii na $W_0^{1,p}(0,1)$

  • Czech description

    Pro spojité funkce $g:[0,1]timesertoer$ dokážeme, že funkcionál $Phi(u)=int_0^1 gbigl(x,u(x)bigr) d x$ je slabě spojitý na $W^{1,p}_0(0,1)$, $1leq p lt infty$, právě tehdy, když $g$ je lineární v druhé proměnné.

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GP201%2F02%2FD111" target="_blank" >GP201/02/D111: Real Analytic Methods in the Calculus of Variations</a><br>

  • Continuities

    Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2005

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Nonlinear analysis - Theory Methods and Applications

  • ISSN

    0362-546X

  • e-ISSN

  • Volume of the periodical

    63

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    7

  • Pages from-to

    81-87

  • UT code for WoS article

  • EID of the result in the Scopus database