Geodesic
Existence theorems for a semilinear elliptic boundary value problem
Annales Polonici Mathematici, Tome 60 (1994) no. 1, pp. 57-67.

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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.
DOI : 10.4064/ap-60-1-57-67
Keywords: elliptic differential inclusions, semilinear elliptic equations, strong solutions

Salvatore Marano 1

1 
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Salvatore Marano. Existence theorems for a semilinear elliptic boundary value problem. Annales Polonici Mathematici, Tome 60 (1994) no. 1, pp. 57-67. doi : 10.4064/ap-60-1-57-67. http://geodesic.mathdoc.fr/articles/10.4064/ap-60-1-57-67/

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