3 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 $\Omega$ be a domain of finite measure, let $\mathbb B$ denote the unit ball in $\mathbb R^d$, and let $\omega_d=|\mathbb B|$. For $m,t\in\mathbb N$, write…

Let $m$ and $\alpha$ be the parameters defining the weighted Sobolev quotient $\mathcal{S}(m,2,\alpha,\alpha,\infty)$, and suppose that this quotient admits a $0$-th nonsingular mi…