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arXiv · 1602.06919

Asymptotic analysis for the Lane-Emden problem in dimension two

Francesca De Marchis·Isabella Ianni·Filomena Pacella
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Abstract

We consider the Lane-Emden Dirichlet problem \begin{equation}\tag{1} \left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }\Omega u=0\qquad\qquad\qquad\mbox{ on }\partial \Omega \end{array}\right. \end{equation} when $p>1$ and $\Omega\subset\mathbb R^2$ is a smooth bounded domain. The aim of the paper is to survey some recent results on the asymptotic behavior of solutions of (1) as the exponent $p\rightarrow \infty $.

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Francesca De Marchis, Isabella Ianni, Filomena Pacella. 2016-02-22. Asymptotic analysis for the Lane-Emden problem in dimension two. https://arxiv.org/abs/1602.06919

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