Regularity of stable solutions of a Lane-Emden type system

2012/06/19 by Craig Cowan, Cowan, Craig
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1206.4273

arxiv created 2012/06/19 · arxiv updated 2012/06/20

Abstract

We examine the system given by \hfill -Δu = λ(v+1)^p Ω \hfill -Δv = γ(u+1)^θ Ω, \hfill u = v =0 ∂ Ω, where λ,γ are positive parameters and where 1 < p ≤ θ and where Ω is a smooth bounded domain in R^N. We show the extremal solutions associated with the above system are bounded provided [(N)/(2) < 1 + (2(θ+1))/(pθ-1) (√((p θ(p+1))/(θ+1)) + √((p θ(p+1))/(θ+1) - √((p θ(p+1))/(θ+1))))]

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