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.
Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs / M. Cozzi, A. Farina, E. Valdinoci. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 293:(2016), pp. 343-381. [10.1016/j.aim.2016.02.014]
Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs
M. Cozzi
;E. ValdinociUltimo
2016
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.
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