The compactness of Moser-Trudinger functionals with conical metric in the unit ball

Qi Xia, Yufeng Lu

Let $\mathbb{B}$ be the unit ball in ${\mathbb{R}}^2$, $W_0^{1,2}\left(\mathbb{B}\right)$ is a standard Sobolev space. Suppose a function $h_{\hat{I}}\mu (x)$ is radially symmetric, nonnegat…