𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The continuity of barrier function with respect to the parameter

✍ Scribed by Xinxiang Li; Jun Yan


Publisher
Coastal and Estuarine Research Federation
Year
2009
Tongue
English
Weight
139 KB
Volume
30
Category
Article
ISSN
1860-6261

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


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.