  We consider inhomogeneous $p$-Laplace type equations of the form
$-\mathrm{div}\left(a(\nabla u)\right)=f$ in a possibly anisotropic setting.
Under general assumptions on the source term $f$, we obtain quantitative
Sobolev regularity results for the stress field $a(\nabla u)$ 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.
