Asymptotics for the best Sobolev constants and their extremal functions

Grey Ercole, Gilberto de Assis Pereira

Let $\Omega$ be a bounded domain of ${\mathbf{R}}^N,$ $N\ge 2.$ Let, for $p>N,$ \[ Λ_{p}(Ω):=\inf\left\{ \left\Vert \nabla u\right\Vert _{p}^{p}:u\in W_{0}^{1,p}(Ω)\quad and\quad\left\V…