On the mean field equation with variable intensities on pierced domains
Pierpaolo Esposito, Pablo Figueroa, Angela Pistoia · IRIS Research product catalog (Sapienza University of Rome) · 2020
We consider the two-dimensional mean field equation of the equilibrium turbulence with variable intensities and Dirichlet boundary condition on a pierced domain −Δu=λ1 [Formula presented] −λ2τ [Formula presented] in Ωε=Ω∖⋃i=1mB(ξi,εi) ̄u=0on ∂Ωε, where B(ξi,εi) is a ball centered at ξi∈Ω with radius εi, τ is a positive parameter and V1,V2>0 are smooth potentials. When λ1>8πm1 and λ2τ2>8π(m−m1) with m1∈0,1,...,m, there exist radii ε1,...,εm small enough such that the problem has a solution which blows-up positively and negatively at the points ξ1,...,ξmjavax.xml.bind.JAXBElement@4bea4a04 and ξmjavax.xml.bind.JAXBElement@8c2344a+1,...,ξm, respectively, as the radii approach zero.