2 problems

Brezis's conjecture. There exist constants $C>0$ and $\delta_0>0$ such that the displayed inequality holds for every continuous $f\in C^0({\mathbb S}^1;{\mathbb S}^1)$ and every…

Let $X_1,X_2,X_3\in\operatorname{Mat}(N\times N,\mathbb{C})$ be self-adjoint operators depending on $N$ and satisfying … Assume that there is a constant $c$ such that … for…