WIAS Preprint No. 2056, (2014)

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


  • Cozzi, Matteo
  • Farina, Alberto
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35J92 35J93 35J20


  • Wulff shapes, energy monotonicity, rigidity and classification results




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 classi?cation 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.

Appeared in

  • Adv. Math., 293 (2016) pp. 343--381.

Download Documents