𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Functions that are mean p-valent with respect to μ-area

✍ Scribed by Yu. E. Alenitsyn


Publisher
SP MAIK Nauka/Interperiodica
Year
1985
Tongue
English
Weight
271 KB
Volume
37
Category
Article
ISSN
0001-4346

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


Integral functionals that are continuous
✍ 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.