Construction of Twice Differentiable Functions with Continuous Laplacian and Bounded Hessian

2022/10/18 by Pan, Yifei, Yan, Yu
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.10099

Abstract

We construct examples of twice differentiable functions in ℝⁿ with continuous Laplacian and bounded Hessian. The same construction is also applicable to higher order differentiability, the Monge-Ampère equation, and mean curvature equation for hypersurfaces.

Related

• Examples of Twice Differentiable Functions in ℝⁿ with Continuous Laplacian and Unbounded Hessian
• On the equivalence of a Hessian-free inequality and Lipschitz continuous Hessian
• Differential geometry in the theory of Hessian operators
• On the Dirichlet problem for a class of augmented Hessian equations
• Hessian equations with elementary symmetric functions