Besov regularity and new error estimates for finite volume approximations of the p-laplacian

In [1], we have constructed a family of finite volume schemes on rectangular meshes for the p-laplacian and we proved error estimates in case the exact solution lies in W2,p. Actually, W2,p is not a natural space for solutions of the p-laplacian in the case p>2. Indeed, for general Lp’ data it can be shown that the solution only belongs to the Besov space [inline-graphic not available: see fulltext]