Definition and existence of renormalized solutions of elliptic equations with general measure data

We introduce a new definition of solution for the nonlinear monotone elliptic problem -div(a(cursive Greek chi, ∇u)) = μ in Ω, u = 0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω. We prove the existence of such a solution, a stability result, and partial uniqueness results.