Partial regularity for a Liouville system

Olivier Goubet, Juan Dávila
2013 Discrete and Continuous Dynamical Systems. Series A  
Let Ω ⊂ R n be a bounded smooth open set. We prove that the singular set of any extremal solution of the system −∆u = µe v , −∆v = λe u in Ω, with u = v = 0 on ∂Ω, µ, λ ≥ 0, has Hausdorff dimension at most n − 10. 2010 Mathematics Subject Classification. Primary: 35G30, 35B65; Secondary: 35P30.
doi:10.3934/dcds.2014.34.2495 fatcat:yums6zpjszgpzmhqrgnep2ndea