Higher Arithmetic $K$-TheoryPublications of the Research Institute for Mathematical Sciences - Tập 41 Số 3 - Trang 599-681 - 2005
Yuichiro Takeda
Weak Solution of a Singular Semilinear Elliptic Equation in a Bounded DomainPublications of the Research Institute for Mathematical Sciences - Tập 41 Số 3 - Trang 793-798 - 2005
Robert Dalmasso
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... hiện toàn bộ