In this talk I will introduce finer counterexamples for the Schauder estimates of elliptic PDE by showing there exist twice differentiable everywhere functions that have continuous Laplacian and unbounded Hessian. It is proved such type examples as well cannot be radial. The textbook example is not twice differentiable at the origin, namely one point singularity difference from above . The idea of construction comes from Complex analysis and the published Paper can be downloaded from

海报.pdf