Finite volume schemes for fully non-linear elliptic equations in divergence form

It is known, see [22], that such equations have unique weak solutions in W 1,p 0 (Ω) (the uniqueness comes from the fact that we consider a monotone operator: a does not depend on ū). These kinds of problem appear for example in the motion of glaciers [21], in flows of incompressible turbulent fluids through porous media [11] or in airfoil design [20]. They also serve as basic references for the mathematical study of fully non-linear elliptic equations (the canonical example being the p-Laplacian: −div(|∇u|p−2∇u) = f).