Existence results for mean field equations

Details Existence results for mean field equations Existence results for mean field equations

1997-10-22

arxiv.org/abs/dg-ga/9710023v3

Mathematics

Differential Geometry

Filling a gap in the argument and adding 2 referrences

Scientific paper

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.

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