The compactness of Moser-Trudinger functionals with conical metric in the unit ball of ${\mathbb{R}}^N$

Qi Xia

Let $\mathbb{B}$ be the unit ball in ${\mathbb{R}}^N$, $W_0^{1,N}\left(\mathbb{B}\right)$ is a standard Sobolev space. Zhang proved the extremal function of the Moser-Trudinger in…