Estimates for Liouville equation with quantized singularities

Juncheng Wei, Lei Zhang

Published 2019-05-10Version 1

For Liouville equations with singular sources, it is well known that blowup solutions may exhibit non-simple blowup phenomenon if the blowup point happens to be the singular source and the strength of the singular source is a multiple of $4\pi$. In this article we prove that even in this case some coefficient functions must vanish at the singular source and bubbling solutions can still be accurately approximated by global solutions.