3 problems

Ramaswamy's conjecture. The fail points occur either at the contact points of the largest inscribed circle or at points of minimal curvature.

Saint-Venant's conjecture. Fail points occur at the contact points of the largest inscribed circle.

Let $\Omega$ be an axially symmetric planar convex domain centered at the origin, and let the fail points be the points where the stress $|\nabla u|$ is maximal, with $u$ the torsi…