Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian (Analysis in Theory and Applications, 2024)
We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded discontinuous Hessian. The same construction is also applicable to higher order differentiability, the Monge-Ampère equation, and the mean curvature equation for hypersurfaces.