2 problems

Let $G\colon [0,\infty)\to\mathbb{R}$ be a solution of … with $G(0)=0$, where $1\le p\le q<\infty$, and vary the initial slope $G'(0)>0$. Critical-slope conjecture. If $G'(0)$ is s…

Let $1le p le q < infty$ and, for each $nin\mathbb{N}$, let $\widetilde{X}^{(n)}=(\widetilde{X}^{(n)}_1,\dots,\widetilde{X}^{(n)}_n)$ be uniformly distributed on…