𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Integral functionals that are continuous with respect to the weak topology on

✍ Scribed by Stanislav Hencl; Jan Kolář; Ondřej Pangrác

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
165 KB
Volume
63
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Integral functionals that are continuous
Integral functionals that are continuous with respect to the weak topology on
✍ Robert Černý; Stanislav Hencl; Jan Kolář 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 685 KB

Let Ω ⊂ R N be a bounded open set and let g: Ω × R → R be a Carathéodory function that satisfies standard growth conditions. Then the functional Φ(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.