11 problems

Non-local modulus of continuity conjecture. Then $\varphi(\cdot,t)$ is a modulus of continuity for $u(\cdot,t)$ on $\Omega\times[0,\infty)$. This proposes that the higher-dimension…

Let $Y=Y_{\alpha,b,H}$ be the fractional Wiener–Weierstrass process, and let $Z_s$ be the random variable arising in the local modulus result referred to as (iii). Non-constant pos…

Let $\omega:(0,1)\to(0,\infty)$ be a modulus of continuity, and consider the prescribed volume form equation … for a density function $f$ on $[0,1]^d$, where…

Gap Conjecture. If the moc of each element of $F$ is subexponential, then the action is topologically conjugate to a smooth ($C^\infty$) action.

Exponential modulus conjecture. The inverse scale function $\delta^{-1}$ is fully exponential in $\epsilon^{-1}$.

Alvisio–Lawler conjecture. There should exist $\beta>0$ such that, on any compact time interval, there almost surely exists a constant $c>0$ for which

Urbano's optimality conjecture. The modulus $r\mapsto |\ln (cr)|^{-\sigma}$ should be optimal for the interior continuity of the temperature in the Stefan problem. The cited work i…

Optimality conjecture. The logarithmic type modulus of continuity should be optimal as a structural property for weak solutions to such partial differential equations. The paper es…

Optimal-modulus conjecture. The modulus of continuity $\omega(r)$ is optimal for solutions of the $p$-degenerate two-phase Stefan problem. The paper derives this modulus, including…

Let $1<p<\infty$ and $1/p<\alpha<1$. For a nondecreasing sequence $\Lambda=\{\lambda_n\}_{n=1}^\infty$ of positive numbers, let $\Lambda BV$ denote the class of functions of bounde…

Let $p\in(1,2)$ and $d\geq 2$, and let $\omega$ be a modulus of continuity. Write $M$ for the uncentered Hardy–Littlewood maximal function and $\|M\|_{\operatorname{Op}(\omega)}$ f…