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

Matteo Cozzi; Alberto  Farina; E. Valdinoci

doi:10.1016/j.aim.2016.02.014

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

Matteo Cozzi
, Alberto Farina
, E. Valdinoci

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

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.

Original language	English
Pages (from-to)	343-381
Number of pages	39
Journal	Advances in Mathematics
Volume	293
DOIs	https://doi.org/10.1016/j.aim.2016.02.014
Publication status	Published - 30 Apr 2016
Externally published	Yes

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10.1016/j.aim.2016.02.014

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title = "Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs",

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.",

author = "Matteo Cozzi and Alberto Farina and E. Valdinoci",

year = "2016",

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doi = "10.1016/j.aim.2016.02.014",

language = "English",

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T1 - Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs

AU - Cozzi, Matteo

AU - Farina, Alberto

AU - Valdinoci, E.

PY - 2016/4/30

Y1 - 2016/4/30

N2 - 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.

AB - 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.

U2 - 10.1016/j.aim.2016.02.014

DO - 10.1016/j.aim.2016.02.014

M3 - Article

SN - 0001-8708

VL - 293

SP - 343

EP - 381

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

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

Abstract

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