Low regularity results for degenerate Poisson problems

In this paper we study the Poisson problem, {−div(dβ∇u)=finΩu=0on∂Ω, where Ω⊂RN, N≥2 is a smooth bounded domain, f is a continuous function, β<1, and d(x)=dist(x,∂Ω). We describe the behaviour of u near ∂Ω and discuss some of its regularity properties.