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MiS Preprint
32/1997
Existence results for mean field equations
Weiyue Ding, Jürgen Jost, Jiayu Li and Guofang Wang
Abstract
Let $\Omega$ be an annulus. We prove that the mean field equation $\begin{array} \displaystyle{-}\Delta \psi & =\frac{e^{-\beta \psi}}{\int_\Omega e^{-\beta \psi }} & in \ \Omega \\ \psi & =0 & on \ \partial \Omega \end{array}$ admits a solution for $ \beta \in (-16 \pi , -8 \ pi)$. This is a supercritical case for the Moser-Trudinger inequality.
