Hessian degeneracy of the torsion function on smooth simply connected nonconvex planar domains

Xiuda Liang, Peng Luo, Wenjie Wang

We construct a family of bounded, smooth, simply connected, nonconvex planar domains ${\Omega }_{a,\epsilon }$. Let $u_{a,\epsilon }$ be the corresponding torsion function satisfying \[ -Δu_{a,ε}=1\quad\t…