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

We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the p-Laplacian kind: -div(vertical bar del u vertical bar(p-2)del u) = f (with 1 < p < infinity). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.