Work

Small-energy regularity for stationary weak solutions of the Liouville equation

Year: 2026

Type: preprint

Abstract: We establish small-energy regularity for stationary weak solutions of the Liouville equation $ -Δu=e^u $ in every dimension. It solves a problem left open in Da Lio [Commun. Partial Differ. Equations, 2008] and posed explicitly again by Da Lio and Hyder in [Commun. Contemp. Math. 2025]. The proof relies on the analysis of concentration phenomena for almost stationary fields with structure constraints.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.26026

Authors: Fu, Haotong, Wang, Kelei, Wang, Wei, Wu, Ke

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G3926134782, G5021052214, G5208386829, G7833826364

OpenAlex ID: W7214117070

Cites:

Cited by:

Related to: 10