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On the modulus of continuity with respect to functions defined on Vilenkin groups

✍ Scribed by S. Fridli


Publisher
Akadmiai Kiad
Year
1985
Tongue
English
Weight
180 KB
Volume
45
Category
Article
ISSN
1588-2632

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Integral functionals that are continuous
✍ Robert ČernΓ½; Stanislav Hencl; Jan KolΓ‘Ε™ πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 685 KB

Let Ω βŠ‚ R N be a bounded open set and let g: Ω Γ— R β†’ R be a CarathΓ©odory function that satisfies standard growth conditions. Then the functional Ξ¦(u) = Ω g (x, u(x)) dx is weakly continuous on W 1,p 0 (Ω), 1 ≀ p ≀ ∞, if and only if g is linear in the second variable.