Asymptotic analysis for the Lane-Emden problem in dimension two

Abstract

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 $\Omega \subset {\mathbb{R}}^2$ 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 $p\to \infty$.

arXiv admin note: substantial text overlap with arXiv:1309.6961