English

A complementary result on a singular mean field equation with a sign-changing potential function

Analysis of PDEs 2024-08-02 v1

Abstract

In this note, we study the singular mean field equation defined on a Riemann surface with a sign-changing potential function. We prove if some singular sources happen to be placed on the zero-level curve of the potential function, a priori estimate can still be obtained. As a consequence of this estimate, existence and multiplicity results can still be obtained based on the topology of the manifold.

Keywords

Cite

@article{arxiv.2408.00036,
  title  = {A complementary result on a singular mean field equation with a sign-changing potential function},
  author = {Lina Wu},
  journal= {arXiv preprint arXiv:2408.00036},
  year   = {2024}
}
R2 v1 2026-06-28T17:59:41.153Z