8 problems

Let $\Omega\subset\mathbb{R}^N$ be a domain with prescribed volume $V(\Omega)=m$, and let the load satisfy $\rho\in L^\infty(\Omega,[-1,1])$. Denote by…

Let $\Omega_c$ be the evolving domain in the clamped plate eigenvalue problem, and let $\lambda_{even}(c)$ and $\lambda_{odd}(c)$ denote the eigenvalues associated with even and od…

Higher-torsional-mode amplitude conjecture. The gap function reduces in amplitude when $\overline f_j$ is in resonance with higher torsional modes.

Let $\Omega$ range over planar domains of unit area, let $\lambda_1(\Omega,\alpha)$ denote the first eigenvalue of the clamped-plate problem under compression parameter $\alpha$, a…

Strip minimaxmax optimum conjecture. The optimum of the minimaxmax problem is the couple $(\overline e_1,\operatorname{Strips})$.

Minimaxmax optimum conjecture. The optimum of the minimaxmax problem is the couple $(f^1,D^0)$.

$L^\infty$ maximizer conjecture. For every $D\subset\Omega$, the unique maximizers of the problem are the odd function

Worst concentrated load conjecture. When $D=\emptyset$, $\overline T_{\pi/2}$ and $-\overline T_{\pi/2}$ are the unique maximizers of the worst case problem.