About: Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$     Goto   Sponge   NotDistinct   Permalink

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Description
  • 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. (en)
  • 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. (cs)
Title
  • 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 $W_0^{1,p}(0,1)$ (cs)
  • Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$ (en)
skos:prefLabel
  • 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 $W_0^{1,p}(0,1)$ (cs)
  • Integral functionals that are continuous with respect to the weak topology on $W_0^{1,p}(0,1)$ (en)
skos:notation
  • RIV/00216208:11320/05:00001490!RIV06-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 81;87
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GP201/02/D111), Z(MSM 113200007)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 525199
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/05:00001490
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Integral; functionals; continuous; respect; topology; $W_0^{1; $ (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [58E332024051]
http://linked.open...i/riv/nazevZdroje
  • Nonlinear analysis - Theory Methods and Applications
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 63
http://linked.open...iv/tvurceVysledku
  • Hencl, Stanislav
  • Kolář, Jan
  • Pangrác, Ondřej
http://linked.open...n/vavai/riv/zamer
issn
  • 0362-546X
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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