Colloquium of the Max Planck Institute: The supercritical Lane-Emden equation and its gradient flow

Colloquium on the occasion of Wolfgang Hackbuschs retirement.In joint work with Simon Blatt and Melanie Rupflin we lay out a functional analytic framework for the Lane-Emden equation $-\mathrm{\Delta }u=u|u{|}^{p-2}$ on an $n$-dimensional domain, $n\ge 3$, in the supercritical regime when $p>\frac{2n}{n-2}$ and study the associated gradient flow.