Existence results for mean field equations
W. Ding, J. Jost, J. Li, G. Wang
dg-gaarXiv:dg-ga/9710023
Abstract
Let Ω be an annulus. We prove that the mean field equation -Δψ=e-βψ∫Ωe-βψ admits a solution with zero boundary for β∈ (-16π,-8π). This is a supercritical case for the Moser-Trudinger inequality.
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