4 problems

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 $\tau>0$ 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