Existence results for mean field equations

W. Ding; J. Jost; J. Li; G. Wang

Existence results for mean field equations

dg-ga 2007-05-23 v3 Differential Geometry

Authors: W. Ding , J. Jost , J. Li , G. Wang

Abstract

Let $\Omega$ be an annulus. We prove that the mean field equation $-\Delta\psi=\frac{e\sp{-\beta\psi}}{\int\sb{\Omega}e\sp{-\beta\psi}}$ admits a solution with zero boundary for $\beta\in (-16\pi,-8\pi)$ . This is a supercritical case for the Moser-Trudinger inequality.

Cite

@article{arxiv.dg-ga/9710023,
  title  = {Existence results for mean field equations},
  author = {W. Ding and J. Jost and J. Li and G. Wang},
  journal= {arXiv preprint arXiv:dg-ga/9710023},
  year   = {2007}
}

Comments

Filling a gap in the argument and adding 2 referrences

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