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

By Matteo Cozzi, Alberto Farina, Enrico Valdinoci. 2014

54 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f38250cc56ae5ec7c5993b8cab4e83d73c43e938