5 problems

Let $\Omega$ be a domain, and consider the Trudinger–Moser functional under a fixed Dirichlet-energy constraint. The preceding non-existence result states that, when $\Omega$ is a…

Wang–Ye's Hardy–Moser–Trudinger conjecture. There exists a finite constant $C(\Omega)>0$ such that

Let $\Omega\subset\mathbb{R}^n$ be a ball, and consider the Trudinger–Moser variational problem … A maximizer is a function attaining this supremum. Uniqueness conjecture. Maximize…

Let $\Omega\subset\mathbb{R}^{2}$ be a bounded domain, let $\psi$ be a weakly continuous functional, and assume that … for every nonzero $u$. Adimurthi's conjecture. The Trudinger–…

Let $H_0^1({\mathbb D})$ be the Sobolev space on the unit disk, let $\eta_\zeta$ denote the disk automorphism associated with $\zeta\in{\mathbb D}$, and let $h_s$ be the radial dil…