Year: 2026
Type: preprint
Abstract: We prove that every concave entire solution of the Liouville equation $-Δu=e^{2u}$ in $\R^n$ is one-dimensional, and we extend the result to a class of general semilinear equations under suitable conditions on the nonlinearity. In dimension two, we also provide a PDE-based proof of the known classification of quasiconcave solutions to planar Liouville solutions, without relying on complex-analytic methods developed in the previous work by Bergweiler-Eremenko-Langley \cite{BEL}
Source: arXiv (Cornell University)
Authors: Gui, Changfeng, Li, Qinfeng, Wang, Chunhua, Xu, Lu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223904389