Worst concentrated load conjecture for the free rectangular plate

Let $\Omega$ be the rectangular plate and let $D$ denote the hinged part of its boundary. Write $\overline T_{\pi/2}$ for the normalized odd concentrated load at the boundary point corresponding to the angle $\pi/2$. When $D=\emptyset$, the free plate case, the relevant worst case problem is the maximization of the gap function over normalized couples of odd concentrated loads.

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.

The conjecture identifies the boundary load expected to produce the largest torsional displacement in the free plate case; the paper states it as an open problem after noting that the corresponding explicit representation is unavailable for more general odd concentrated loads.