Saint-Venant's conjecture on fail points

Let $\Omega$ be a convex planar domain symmetric about the two coordinate axes. A fail point is a point where $|\nabla u_{\Omega}|$ attains its maximum, where $u_{\Omega}$ is the torsion function. The largest inscribed circle is a circle of maximal radius contained in $\Omega$.

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

Kawohl proved this under the additional assumption that the curvature on $\partial\Omega$ is monotonic in the first quadrant. Ramaswamy and Sweers later disproved the conjecture by constructing domains symmetric about two axes whose long and short axes have equal length but whose endpoints have different curvatures.