Given N ≥ 2, we completely classify solutions to the anisotropic -Liouville equation (formula presented) under the finite mass condition (formula presented). Here ΔHN is the so-called Finsler N-Laplacian induced by a positively homogeneous function H. As a consequence in the planar case N=2, we give an affirmative answer to a conjecture made in [53].
Classification of Solutions to the Anisotropic N-Liouville Equation in ℝN [Classification of Solutions to the Anisotropic N-Liouville Equation in ℝᴺ] / G. Ciraolo, X. Li. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2024:19(2024 Oct), pp. 12824-12856. [10.1093/imrn/rnae181]
Classification of Solutions to the Anisotropic N-Liouville Equation in ℝN [Classification of Solutions to the Anisotropic N-Liouville Equation in ℝᴺ]
G. Ciraolo
Primo
;X. LiUltimo
2024
Abstract
Given N ≥ 2, we completely classify solutions to the anisotropic -Liouville equation (formula presented) under the finite mass condition (formula presented). Here ΔHN is the so-called Finsler N-Laplacian induced by a positively homogeneous function H. As a consequence in the planar case N=2, we give an affirmative answer to a conjecture made in [53].
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