6 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 $\Omega$ be the bounded domain in the nonlocal Poisson problem, let $u$ solve that problem, let $f\in L^2(\Omega)$, and let $\beta$ be the kernel exponent. Continuity conjectur…

Masoero–Raimondo string-equation conjecture. Under the nonvanishing assumption, $U(T,X)$ is a global solution of this equation.

Assume that $f_a(u)=u(1-u)(u-a)$ with $0<a<1/2$. Let $\mathcal{K}$ satisfy the stated hypotheses with normalized second moment … Let $\mathcal{R}_j$, $j=1,\ldots,5$, be the regions…

Assume that $\mathcal{K}(x)=\mathrm{e}^{-|x|}/2$ and that $f_a(u)=u(1-u)(u-a)$ with $0<a<1/2$. Let $(a,d)\in \mathcal{R}_2\cup\mathcal{R}_3$ such that $0<\ell_1^*<\infty$ is well d…

Let the linear hull in Proposition be the span of the relevant exponential solutions, and let its closure be taken in the function space under consideration. Closure conjecture. Pr…