Asymptotic analysis for the Lane-Emden problem in dimension two

We consider the Lane-Emden Dirichlet problem \begin{equation}\tag{1} \left\{\begin{array}{lr}-Δu= |u|^{p-1}u\qquad \mbox{ in }Ωu=0\qquad\qquad\qquad\mbox{ on }\partial Ω\end{array}\right. \end{equation} when $p>1$ and $Ω\subset\mathbb R^2$ 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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