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
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DOI - Digital Object Identifier
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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
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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
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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
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EID of the result in the Scopus database
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