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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F05%3A00001490%21RIV06-MSM-11320___
rdf:type
skos:Concept n16:Vysledek
dcterms:description
Pro spojité funkce $g:[0,1]\times\er\to\er$ dokážeme, že funkcionál $\Phi(u)=\int_0^1 g\bigl(x,u(x)\bigr) \d x$ je slabě spojitý na $W^{1,p}_0(0,1)$, $1\leq p lt \infty$, právě tehdy, když $g$ je lineární v druhé proměnné. For continuous functions $g:[0,1]\times\er\to\er$ we prove that the functional $\Phi(u)=\int_0^1 g\bigl(x,u(x)\bigr) \d x$ is weakly continuous on $W^{1,p}_0(0,1)$, $1\leq p lt \infty$, if and only if $g$ is linear in the second variable. For continuous functions $g:[0,1]\times\er\to\er$ we prove that the functional $\Phi(u)=\int_0^1 g\bigl(x,u(x)\bigr) \d x$ is weakly continuous on $W^{1,p}_0(0,1)$, $1\leq p lt \infty$, if and only if $g$ is linear in the second variable.
dcterms:title
Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$ Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$ Integrální funkcionály, které jsou spojité vyhledem ke slabé topologii na $W_0^{1,p}(0,1)$
skos:prefLabel
Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$ Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$ Integrální funkcionály, které jsou spojité vyhledem ke slabé topologii na $W_0^{1,p}(0,1)$
skos:notation
RIV/00216208:11320/05:00001490!RIV06-MSM-11320___
n3:strany
81;87
n3:aktivita
n11:Z n11:P
n3:aktivity
P(GP201/02/D111), Z(MSM 113200007)
n3:cisloPeriodika
1
n3:dodaniDat
n4:2006
n3:domaciTvurceVysledku
n12:8100624 n12:4342887 n12:9844910
n3:druhVysledku
n14:J
n3:duvernostUdaju
n13:S
n3:entitaPredkladatele
n17:predkladatel
n3:idSjednocenehoVysledku
525199
n3:idVysledku
RIV/00216208:11320/05:00001490
n3:jazykVysledku
n19:eng
n3:klicovaSlova
Integral; functionals; continuous; respect; topology; $W_0^{1; $
n3:klicoveSlovo
n6:%24 n6:%24W_0%5E%7B1 n6:functionals n6:Integral n6:topology n6:respect n6:continuous
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[58E332024051]
n3:nazevZdroje
Nonlinear analysis - Theory Methods and Applications
n3:obor
n9:BA
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
3
n3:projekt
n7:GP201%2F02%2FD111
n3:rokUplatneniVysledku
n4:2005
n3:svazekPeriodika
63
n3:tvurceVysledku
Hencl, Stanislav Pangrác, Ondřej Kolář, Jan
n3:zamer
n15:MSM%20113200007
s:issn
0362-546X
s:numberOfPages
7
n18:organizacniJednotka
11320