- Tytuł:
- Existence theorems for a semilinear elliptic boundary value problem
- Autorzy:
- Marano, Salvatore
- Powiązania:
- https://bibliotekanauki.pl/articles/1311657.pdf
- Data publikacji:
- 1994
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
elliptic differential inclusions
semilinear elliptic equations
strong solutions - Opis:
- Let Ω be a bounded domain in $ℝ^n$, n ≥ 3, with a smooth boundary ∂Ω; let L be a linear, second order, elliptic operator; let f and g be two real-valued functions defined on Ω × ℝ such that f(x,z) ≤ g(x,z) for almost every x ∈ Ω and every z ∈ ℝ. In this paper we prove that, under suitable assumptions, the problem { f(x,u) ≤ Lu ≤ g(x,u) in Ω, u = 0 on ∂Ω, has at least one strong solution $u ∈ W^{2,p}(Ω) ∩ W^{1,p}_0(Ω). Next, we present some remarkable special cases.
- Źródło:
-
Annales Polonici Mathematici; 1994-1995, 60, 1; 57-67
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł