3 problems

Let $k$ be a positive integer, let $n\in\{2k+1,2k+2,\ldots,4k-1\}$, and consider the higher-order Brézis–Nirenberg problem on a Euclidean ball $\Omega=B^n$: … where…

Exponential turnpike conjecture. There are constants $K>0$ and $\mu>0$, independent of $T$, such that

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…