10 problems

Fix $b1 eq 0$?

Uniform boundedness conjecture. There is a universal constant $B_{V_0,R_0}$ such that

Uniform observability conjecture. For every $T>0$, there exists a constant $C=C(X,S,T)>0$ such that the observability inequality holds. Moreover, the constant can be chosen to depe…

For each $d\geq 1$, let $Y$ be the normed function space introduced in the paper for Schrödinger-wave observability, and let $Y_0$ denote the closure of continuous functions in $Y$…

Harmonic-oscillator phase-retrieval conjecture. If $|u(t,x)|=|v(t,x)|$ for every $t\in\mathbb{R}$ and every $x\in\mathbb{R}^d$, then there exists $c\in\mathbb{R}$ such that…

Let $\Omega$ be either $\mathbb{R}^N$ or an exterior domain in $\mathbb{R}^N$, and let $V\in L^{\infty}(\mathbb{R}^N)$ satisfy $\|V\|_{\infty}\leq 1$. Suppose that $u$ solves … and…

Let $\tilde{\Delta}:=\frac{1}{2\pi}(\partial_{11}+\alpha\partial_{22})$ on $\mathbb{T}^2$, where $\alpha<0$ is irrational, and let $e^{it\tilde{\Delta}}f$ denote the solution to…

Let $N$ be a positive integer, let $(a_n)_{n=1}^N$ satisfy … and let $\lambda$ satisfy $N^{\frac14}\leq\lambda\leq N^{\frac12}$. Periodic Schrödinger maximal-function level set con…

“Qualitative” Landis conjecture. Then $u\equiv 0$.

Higher-dimensional space-time estimate. Then