The non-local mean-field equation on an interval

2018/12/05 by DelaTorre, Azahara, Hyder, Ali, Martinazzi, Luca +1
#35B44 #35C15 #35J61 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.02165

Abstract

We consider the fractional mean-field equation on the interval I=(-1,1) (-Δ)^(1)/(2) u=ρ\frace^u∫_Ie^udx, subject to Dirichlet boundary conditions, and prove that existence holds if and only if ρ<2π. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of non-local type.

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