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

Matteo Cozzi (1) , Alberto Farina (1) , Enrico Valdinoci

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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. (C) 2016 Elsevier Inc. All rights reserved.

Domaines: Mathématiques [math]

Matteo Cozzi, Alberto Farina, Enrico Valdinoci. Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs. Advances in Mathematics, 2016, 293, pp.343-381. ⟨10.1016/j.aim.2016.02.014⟩. ⟨hal-03621420⟩