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. 
Matteo Cozzi, Alberto Farina, Enrico Valdinoci
math.AP