Interior regularity results for inhomogeneous anisotropic quasilinear equations

We consider inhomogeneous p-Laplace type equations of the form -div (a del u)) = f in a possibly anisotropic setting. Under general assumptions on the source term f, we obtain quantitative Sobolev regularity results for the stress field a(del u) and weighted L-2 estimates for the Hessian of the solution. As far as we know, our results are new or refine the ones available in literature also when restricted to the Euclidean setting.