"Integral functionals that are continuous with respect to the weak topology on W-0(1,p)(Omega)"@en . "11"^^ . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . . . "Integral functionals that are continuous with respect to the weak topology on W-0(1,p)(Omega)" . "Integral functionals that are continuous with respect to the weak topology on W-0(1,p)(Omega)"@en . "319792" . "Kol\u00E1\u0159, Jan" . . "Nonlinear Analysis: Theory, Methods & Applications" . "[94A7C30FB3C7]" . . . "7-8" . . "RIV/67985840:_____/09:00330850" . "000267405300036" . . . "Integral functionals that are continuous with respect to the weak topology on W-0(1,p)(Omega)" . . "71" . "Hencl, S." . "3"^^ . . "Let Omega subset of N-R be a bounded open set and let g: Omega x R -> R be a Caratheodory function that satisfies standard growth conditions. Then the functional Phi(u) = integral(Omega) g (x, u(x)) dx is weakly continuous on W-0(1,p)(Omega), 1 <= p <= infinity, if and only if g is linear in the second variable."@en . . "weak continuity; nonlinear integral functional; Sobolev spaces; linearity"@en . "\u010Cern\u00FD, R." . . "Let Omega subset of N-R be a bounded open set and let g: Omega x R -> R be a Caratheodory function that satisfies standard growth conditions. Then the functional Phi(u) = integral(Omega) g (x, u(x)) dx is weakly continuous on W-0(1,p)(Omega), 1 <= p <= infinity, if and only if g is linear in the second variable." . "P(GA201/06/0018), P(GP201/06/P100), Z(AV0Z10190503), Z(MSM0021620839)" . "1"^^ . . . . . "RIV/67985840:_____/09:00330850!RIV10-AV0-67985840" . "0362-546X" . . . . .