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arXiv · 1412.6561

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

Matteo Cozzi·Alberto Farina·Enrico Valdinoci
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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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Matteo Cozzi, Alberto Farina, Enrico Valdinoci. 2014-12-19. Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs. https://doi.org/10.1016/j.aim.2016.02.014

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