10 problems

Let $\Omega\subset\mathbb{R}^n$, with $n\geq 2$, be a convex domain, and let $C(\Omega)$ denote a positive constant for which … where…

Let $B$ be a ball and let $d4b\Omega\subset\mathbb{R}^N$ be a domain. Denote by $d706_{1,p}(\Omega)$ the first eigenvalue of the Dirichlet $p$-Laplacian on $d4b\Omega$, and by…

Let $\Omega\subset\mathbb R^d$ be a domain of finite measure, and let $\lambda_k^{(m,t)}(\Omega)$ denote its $k$th buckling eigenvalue. Generalised Payne buckling inequality. For e…

Let $u=gamma$ be the Gaussian measure, let $L=-Deltagamma$ be the Ornstein–Uhlenbeck operator, and let $d(Omega)$ be the Gaussian Fraenkel asymmetry. The quantitative Gaussian Fab…

Let $H=-\triangle+|x|^\beta$ on $\mathbb R^n$, where $\beta>0$. Let $\Omega\subset\mathbb R^n$ be a measurable sensor set satisfying the equidistribution condition … for every…

Let $m,l\five in\text{N}$, and let $P_lambda$ be the spectral projector for the Shubin operator $H=(-Delta)^m+|x|^{2l}$. Suppose that $omega\five subset\real^d$ satisfies the decay…

Let $\tau>0$ and let $\function{P}_\tau$ denote the spectral projector associated with $-Delta+|x|^\tau$. Suppose that $omega\five subset\real^d$ is measurable and that, for some…

Let $\Omega$ be a bounded domain in $\mathbb R^d$ with smooth boundary. Let $\lambda_j$, $\Lambda_j$, and $\sigma_j$ denote the eigenvalues used in the paper for the Dirichlet Lapl…

Bhattacharya–Weitsman–Nadirashvili conjecture. There exists a dimensional constant $C>0$ such that

Two-impediments conjecture. There are only two impediments to the existence of such a family, and therefore to a weakened quadratic inequality of the form: unless a quantum graph c…