Abstract
Let
Ω
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
β∈(−16π,−8π)
. This is a supercritical case for the Moser-Trudinger inequality.
Related Researches
Submitted on 22 Oct 1997 (v1), last revised 30 Nov 1997 (this version, v3)
Updated
arXiv.org
Original Source