3 problems

Let $n\geq 3$, let $\mathbb{R}^n_+=\{x=(x',x_n)\in\mathbb{R}^n:x_n>0\}$, and let $\mathbb{S}^{n-1}_+=\{\theta\in\mathbb{S}^{n-1}:\theta_n>0\}$. For a solution $u$ of the critical D…

Capacity-dependence conjecture. The limit

Let $\Omega \subset \mathbb{R}^N$ be a smooth bounded domain, and let $q_1$ and $q_2$ be the exponents defined in the paper. A positive solution is a function…