9 problems

Let $D\subset\mathbb{R}^2$ be a bounded simply connected domain with sufficiently smooth boundary, and let $v\in C^4(D)\cap C^1(\overline D)$. The boundary conditions use the inwar…

The delayed forward stochastic control problem involves a controlled forward system with state delays, while problem (O) is the corresponding control problem considered in the pape…

Normal derivative conjecture. Such a weakened normal derivative lemma should hold for ${\cal L}$.

Let $U$ be a bounded domain with smooth boundary in $\mathbb{R}^N$, let $s\in(0,\frac{3}{2})$, and consider the variational Dirichlet problem for the higher-order fractional Laplac…

Let $M$, $\beta$, $\theta$, $\rho$, $u$, $b$, and the conditions defining the range … be as in Theorem … is replaced by … , but the supplied text gives no resolution or further co…

Sign conjecture for $K_0$. The kernel satisfies

Let $U_T$ be the spacetime domain, let $U_{(x,t)}$ be the backwards light cone of $(x,t)\in U_T$, and let $\widetilde{Q}$ be the spatial operator in the relativistic heat equation.…

Let $U_T$ be the spacetime domain, let $U_{(x,t)}$ denote the backwards light cone … and let $\widetilde{Q}$ be the spatial operator in the relativistic heat equation. Strong maxim…

Hmidi's conjecture. The maximum principle should hold for all dimensions $d\ge 1$ and the full range