Year: 2005
Type: article
Abstract: We study the singular semilinear elliptic equation ∆u + f(., u) = 0 in \mathcal D'(Ω) , where Ω ⊂ ℝ^n ( n ≥ 1 ) is a bounded domain of class C^{1,1}. f : Ω × (0, ∞) → [0, ∞) is such that f(., u) \in L^1(Ω) for u > 0 and u → f(x, u) is continuous and nonincreasing for a.e. x in Ω . We assume that there exists a subset Ω' ⊂ Ω with positive measure such that f(x, u) > 0 for x\in Ω' and u > 0 and that ∫_Ω f(x, cd(x, ∂Ω))dx < ∞ for all c > 0 . Then we show that there exists a unique solution u in W_0^{1,1}(Ω) such that ∆u\in L^1(Ω) , u > 0 a.e. in Ω .
Author: Robert Dalmasso
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1978632016