Sharp singular Moser-Trudinger inequalities and n-Laplacian equations with degenerate potentials

Hao Hu, Yanjun Liu, Huabo Zhang

Let $n\ge 2$, $0<\beta <n$, and let $V$ be a continuous nonnegative potential on ${\mathbb{R}}^n$ with a positive lower bound outside a ball. Under the constraint $\int_{\R^n}(|\nabla u|^n+V|u|^n…