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arXiv · 1206.4273

Regularity of stable solutions of a Lane-Emden type system

Craig Cowan
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Abstract

We examine the system given by \hfill -Δu = λ(v+1)^p \qquad Ω \hfill -Δv = γ(u+1)^θ\qquad Ω, \hfill u = v =0 \qquad \quad \partial Ω, where $ λ,γ$ are positive parameters and where $ 1 < p \le 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 [\frac{N}{2} < 1 + \frac{2(θ+1)}{pθ-1} (\sqrt{\frac{p θ(p+1)}{θ+1}} + \sqrt{\frac{p θ(p+1)}{θ+1} - \sqrt{\frac{p θ(p+1)}{θ+1}}})]

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Craig Cowan. 2012-06-19. Regularity of stable solutions of a Lane-Emden type system. https://arxiv.org/abs/1206.4273

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