4 problems

Let $\Omega$ be a bounded domain with smooth boundary in an $n$-dimensional Riemannian manifold, and let $0<\Lambda_1\leq\Lambda_2\leq\cdots$ be the successive eigenvalues of the o…

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 $\Omega$ 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…

Let $\Omega$ be a bounded domain in $\mathbb R^d$ with smooth boundary. Let $N(z)$ denote the counting function for the eigenvalues of the buckling problem, and let $B_k$ denote th…