Regularizing effect in singular semilinear problems

Abstract

We analyze how different relations in the lower order terms lead to the same regularizing effect on singular problems whose model is −∆u+g(x, u) = f(x)/uγ in Ω, u = 0 on ∂Ω, where Ω is a bounded open set of R N , γ > 0, f(x) is a nonnegative function in L 1 (Ω) and g(x, s) is a Carath´eodory function. In a framework where no H1 0 (Ω) solution is expected, we prove its existence (regularizing effect) whenever the datum f interacts conveniently either with the boundary of the domain or with the lower order term.