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. Li
Ultimo
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].
Settore MATH-03/A - Analisi matematica
   Partial differential equations and related geometric-functional inequalities.
   MINISTERO DELL'UNIVERSITA' E DELLA RICERCA
   20229M52AS_004
ott-2024
2-set-2024
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1117488
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