Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs

We consider possibly degenerate and singular elliptic equations in a possibly anisotropic medium.We obtain monotonicity results for the energy density, rigidity results for the solutions and classification results for the singularity/degeneracy/anisotropy allowed.As far as we know, these results are new even in the case of non-singular and non-degenerate anisotropic equations.