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.

References in corpus (1)

• Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations

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• Remark on a special class of Finsler $p$-Laplacian equation
• Extremal solution and Liouville theorem for anisotropic elliptic equations
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