A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems

Abstract

We consider model semilinear elliptic equations of the type{−div(A(x)∇u)=σu−λ,u>0inΩ,u∈H01(Ω), where Ω is a bounded domain in RN, N≥1, A∈L∞(Ω)N×N is a coercive matrix, 0<λ≤1 and σ is a nonnegative function in Lloc1(Ω), or more generally, nonnegative Radon measure on Ω. We discuss H01(Ω)-stability of u under a minimal assumption on σ and apply the result to homogenization problems.