A sign-changing Liouville equation

Abstract

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