Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Catino - Dario Daniele Monticelli - A. Roncoroni

On the critical $p$-Laplace equation

created by catino on 17 Oct 2023



Inserted: 17 oct 2023
Last Updated: 17 oct 2023

Year: 2022

ArXiv: 2204.06940 PDF


In this paper we provide the classification of positive solutions to the critical $p-$Laplace equation on $\mathbb{R}^n$, for $1<p<n$, possibly having infinite energy. If $n=2$, or if $n=3$ and $\frac 32<p<2$ we prove rigidity without any further assumptions. In the remaining cases we obtain the classification under energy growth conditions or suitable control of the solutions at infinity. Our assumptions are much weaker than those already appearing in the literature. We also discuss the extension of the results to the Riemannian setting.

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