TY - JOUR
T1 - Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian
AU - Pan , Yifei
AU - Yan , Yu
JO - Analysis in Theory and Applications
VL - 3
SP - 311
EP - 334
PY - 2024
DA - 2024/10
SN - 40
DO - http://doi.org/10.4208/ata.OA-2024-0017
UR - https://global-sci.org/intro/article_detail/ata/23468.html
KW - Twice differentiable, continuous Laplacian, bounded Hessian.
AB - <p style="text-align: justify;">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.</p>