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Integral functionals that are continuous with respect to the weak topology on W-0(1,p)(Omega)

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    0330850 - MÚ 2010 RIV GB eng J - Journal Article
    Černý, R. - Hencl, S. - Kolář, Jan
    Integral functionals that are continuous with respect to the weak topology on W-0(1,p)(Omega).
    [Integrální funkcionály spojité vzhledem ke slabé topologii na W_0^{1,p}(Omega).]
    Nonlinear Analysis: Theory, Methods & Applications. Roč. 71, 7-8 (2009), s. 2753-2763. ISSN 0362-546X. E-ISSN 1873-5215
    R&D Projects: GA ČR GA201/06/0018
    Institutional research plan: CEZ:AV0Z10190503
    Keywords : weak continuity * nonlinear integral functional * Sobolev spaces * linearity
    Subject RIV: BA - General Mathematics
    Impact factor: 1.487, year: 2009

    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.

    Nechť (Omega) je omezená množina v N-R a nechť g : (Omega) x R -> R je Caratheodoryovská funkce splňující standardní růstové podmínky. Pak je funkcionál Phi(u) = integral(Omega) g (x, u(x)) dx slabě spojitý na W-0(1,p)(Omega), 1 <= p <= infty právě tehdy, když je g lineární ve druhé proměnné.
    Permanent Link: http://hdl.handle.net/11104/0176538

     
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