Generalised Rayleigh–Faber–Krahn inequality for polyharmonic eigenvalues

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 $\lambda_{1}^{(m,t)}(\Omega)$ for the first eigenvalue of the buckling problem in the paper. Generalised Rayleigh–Faber–Krahn inequality. For any domain $\Omega$ of finite measure,

$$|\Omega|^{2t/d}\lambda_{1}^{(m,t)}(\Omega)\geq \omega_d^{2t/d}\lambda_{1}^{(m,t)}(\mathbb B).$$

This conjecture proposes that the ball minimises the volume-normalised first eigenvalue. Its status is not resolved in the supplied source.