A sign-changing Liouville Equation

2014/10/03 by Alejandro Sarria, Sarria, Alejandro, Ralph Saxton +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.1410.0749

Submitted

arxiv created 2014/10/03 · openalex publication_date 2014/10/03 · arxiv updated 2014/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine periodic solutions to an initial boundary value problem for a Liouville equation with sign-changing weight. A representation formula is derived both for singular and nonsingular boundary data, including data arising from fractional linear maps. In the case of singular boundary data we study the effects the induced singularity has on the interior regularity of solutions. Regularity criteria are also found for a generalized form of the equation.

Citations

• The Schwarzian derivative for harmonic mappings

Related

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• Liouville equation under perturbation
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• Liouville theorem for singular solutions to nonlocal equations